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Volume 7
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Risks, Volume 7, Issue 3 (September 2019) – 28 articles

Cover Story (view full-size image): Long-term care (LTC) encompasses a set of services provided to impaired and dependent elderly people. Such help can be provided as informal care by relatives and as formal care by professionals. The aim of the research by Rudnytskyi and Wagner was to study individual characteristics that relate to demand for LTC in Switzerland and to the substitutional or complementary relation of both types of care. View this paper.
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18 pages, 464 KiB  
Article
Coherent-Price Systems and Uncertainty-Neutral Valuation
by Patrick Beissner
Risks 2019, 7(3), 98; https://doi.org/10.3390/risks7030098 - 17 Sep 2019
Viewed by 2360
Abstract
This paper considers fundamental questions of arbitrage pricing that arises when the uncertainty model incorporates ambiguity about risk. This additional ambiguity motivates a new principle of risk- and ambiguity-neutral valuation as an extension of the paper by Ross (1976) (Ross, Stephen A. 1976. [...] Read more.
This paper considers fundamental questions of arbitrage pricing that arises when the uncertainty model incorporates ambiguity about risk. This additional ambiguity motivates a new principle of risk- and ambiguity-neutral valuation as an extension of the paper by Ross (1976) (Ross, Stephen A. 1976. The arbitrage theory of capital asset pricing. Journal of Economic Theory 13: 341–60). In the spirit of Harrison and Kreps (1979) (Harrison, J. Michael, and David M. Kreps. 1979. Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory 20: 381–408), the paper establishes a micro-economic foundation of viability in which ambiguity-neutrality imposes a fair-pricing principle via symmetric multiple prior martingales. The resulting equivalent symmetric martingale measure set exists if the uncertain volatility in asset prices is driven by an ambiguous Brownian motion. Full article
(This article belongs to the Special Issue Financial Risks and Regulation)
12 pages, 471 KiB  
Article
DeepTriangle: A Deep Learning Approach to Loss Reserving
by Kevin Kuo
Risks 2019, 7(3), 97; https://doi.org/10.3390/risks7030097 - 16 Sep 2019
Cited by 28 | Viewed by 7010
Abstract
We propose a novel approach for loss reserving based on deep neural networks. The approach allows for joint modeling of paid losses and claims outstanding, and incorporation of heterogeneous inputs. We validate the models on loss reserving data across lines of business, and [...] Read more.
We propose a novel approach for loss reserving based on deep neural networks. The approach allows for joint modeling of paid losses and claims outstanding, and incorporation of heterogeneous inputs. We validate the models on loss reserving data across lines of business, and show that they improve on the predictive accuracy of existing stochastic methods. The models require minimal feature engineering and expert input, and can be automated to produce forecasts more frequently than manual workflows. Full article
(This article belongs to the Special Issue Claim Models: Granular Forms and Machine Learning Forms)
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7 pages, 312 KiB  
Editorial
Special Issue “Risk, Ruin and Survival: Decision Making in Insurance and Finance”
by Jiandong Ren, Kristina Sendova and Ričardas Zitikis
Risks 2019, 7(3), 96; https://doi.org/10.3390/risks7030096 - 07 Sep 2019
Cited by 2 | Viewed by 2967
Abstract
It has been six years since Editor-in-Chief Steffensen (2013) wrote in his editorial that “to Risks inclusiveness, inter-disciplinarity, and open-mindedness is the very starting point [...] Full article
(This article belongs to the Special Issue Risk, Ruin and Survival: Decision Making in Insurance and Finance)
11 pages, 706 KiB  
Article
Penalising Unexplainability in Neural Networks for Predicting Payments per Claim Incurred
by Jacky H. L. Poon
Risks 2019, 7(3), 95; https://doi.org/10.3390/risks7030095 - 01 Sep 2019
Cited by 2 | Viewed by 3211
Abstract
In actuarial modelling of risk pricing and loss reserving in general insurance, also known as P&C or non-life insurance, there is business value in the predictive power and automation through machine learning. However, interpretability can be critical, especially in explaining to key stakeholders [...] Read more.
In actuarial modelling of risk pricing and loss reserving in general insurance, also known as P&C or non-life insurance, there is business value in the predictive power and automation through machine learning. However, interpretability can be critical, especially in explaining to key stakeholders and regulators. We present a granular machine learning model framework to jointly predict loss development and segment risk pricing. Generalising the Payments per Claim Incurred (PPCI) loss reserving method with risk variables and residual neural networks, this combines interpretable linear and sophisticated neural network components so that the ‘unexplainable’ component can be identified and regularised with a separate penalty. The model is tested for a real-life insurance dataset, and generally outperformed PPCI on predicting ultimate loss for sufficient sample size. Full article
(This article belongs to the Special Issue Claim Models: Granular Forms and Machine Learning Forms)
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41 pages, 2510 KiB  
Article
Optimal Stopping and Utility in a Simple Modelof Unemployment Insurance
by Jason S. Anquandah and Leonid V. Bogachev
Risks 2019, 7(3), 94; https://doi.org/10.3390/risks7030094 - 01 Sep 2019
Cited by 2 | Viewed by 3932
Abstract
Managing unemployment is one of the key issues in social policies. Unemployment insurance schemes are designed to cushion the financial and morale blow of loss of job but also to encourage the unemployed to seek new jobs more proactively due to the continuous [...] Read more.
Managing unemployment is one of the key issues in social policies. Unemployment insurance schemes are designed to cushion the financial and morale blow of loss of job but also to encourage the unemployed to seek new jobs more proactively due to the continuous reduction of benefit payments. In the present paper, a simple model of unemployment insurance is proposed with a focus on optimality of the individual’s entry to the scheme. The corresponding optimal stopping problem is solved, and its similarity and differences with the perpetual American call option are discussed. Beyond a purely financial point of view, we argue that in the actuarial context the optimal decisions should take into account other possible preferences through a suitable utility function. Some examples in this direction are worked out. Full article
(This article belongs to the Special Issue Applications of Stochastic Optimal Control to Economics and Finance)
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14 pages, 428 KiB  
Article
Nash Bargaining Over Margin Loans to Kelly Gamblers
by Alex Garivaltis
Risks 2019, 7(3), 93; https://doi.org/10.3390/risks7030093 - 27 Aug 2019
Cited by 1 | Viewed by 2645
Abstract
I derive practical formulas for optimal arrangements between sophisticated stock market investors (continuous-time Kelly gamblers or, more generally, CRRA investors) and the brokers who lend them cash for leveraged bets on a high Sharpe asset (i.e., the market portfolio). Rather than, say, the [...] Read more.
I derive practical formulas for optimal arrangements between sophisticated stock market investors (continuous-time Kelly gamblers or, more generally, CRRA investors) and the brokers who lend them cash for leveraged bets on a high Sharpe asset (i.e., the market portfolio). Rather than, say, the broker posting a monopoly price for margin loans, the gambler agrees to use a greater quantity of margin debt than he otherwise would in exchange for an interest rate that is lower than the broker would otherwise post. The gambler thereby attains a higher asymptotic capital growth rate and the broker enjoys a greater rate of intermediation profit than would be obtained under non-cooperation. If the threat point represents a complete breakdown of negotiations (resulting in zero margin loans), then we get an elegant rule of thumb: r L * = 3 / 4 r + 1 / 4 ν − σ 2 / 2 , where r is the broker’s cost of funds, ν is the compound-annual growth rate of the market index, and σ is the annual volatility. We show that, regardless of the particular threat point, the gambler will negotiate to size his bets as if he himself could borrow at the broker’s call rate. Full article
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20 pages, 506 KiB  
Article
Drivers of Old-Age Dependence and Long-Term Care Usage in Switzerland—A Structural Equation Model Approach
by Iegor Rudnytskyi and Joël Wagner
Risks 2019, 7(3), 92; https://doi.org/10.3390/risks7030092 - 26 Aug 2019
Cited by 5 | Viewed by 4480
Abstract
Long-term care (LTC) encompasses a set of services provided to impaired and dependent elderly people. To assess the level of the dependence several scales are used, including activities of daily living (ADL), instrumental ADL (IADL) and functional limitations. Once an elderly person fails [...] Read more.
Long-term care (LTC) encompasses a set of services provided to impaired and dependent elderly people. To assess the level of the dependence several scales are used, including activities of daily living (ADL), instrumental ADL (IADL) and functional limitations. Once an elderly person fails to perform these activities independently, he or she requires special assistance. Help can be provided as informal care by relatives and as formal care by professionals. The aim of this research is to study individual characteristics that relate to the demand of LTC and to analyze the relation between formal and informal care. We base our study on data from the Swiss Health Survey focusing on respondents aged over 65 years. Using the structural equation modeling technique, we develop a statistical model that considers the dependence concept as a latent variable. This hidden dependence variable combines three indices linked to the limitations in ADL, in IADL and functional limitations. Accounting for causality links between covariates enables us to include the indirect effect of pathologies on the receipt of LTC mediated via dependence. In our model, we do not assume a causal relationship between formal and informal care. From our results, we observe a significant impact of pathologies as well as of the socio-demographic factors on the demand for LTC. The relationship between formal and informal care is found to be of both a complementary and substitutional nature. Full article
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18 pages, 1049 KiB  
Article
Bigger Is Not Always Safer: A Critical Analysis of the Subadditivity Assumption for Coherent Risk Measures
by Hans Rau-Bredow
Risks 2019, 7(3), 91; https://doi.org/10.3390/risks7030091 - 26 Aug 2019
Cited by 4 | Viewed by 3939
Abstract
This paper provides a critical analysis of the subadditivity axiom, which is the key condition for coherent risk measures. Contrary to the subadditivity assumption, bank mergers can create extra risk. We begin with an analysis how a merger affects depositors, junior or senior [...] Read more.
This paper provides a critical analysis of the subadditivity axiom, which is the key condition for coherent risk measures. Contrary to the subadditivity assumption, bank mergers can create extra risk. We begin with an analysis how a merger affects depositors, junior or senior bank creditors, and bank owners. Next it is shown that bank mergers can result in higher payouts having to be made by the deposit insurance scheme. Finally, we demonstrate that if banks are interconnected via interbank loans, a bank merger could lead to additional contagion risks. We conclude that the subadditivity assumption should be rejected, since a subadditive risk measure, by definition, cannot account for such increased risks. Full article
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13 pages, 555 KiB  
Article
Persistence of Bank Credit Default Swap Spreads
by Xin Huang
Risks 2019, 7(3), 90; https://doi.org/10.3390/risks7030090 - 26 Aug 2019
Cited by 3 | Viewed by 2862
Abstract
Credit default swap (CDS) spreads measure the default risk of the reference entity and have been frequently used in recent empirical papers. To provide a rigorous econometrics foundation for empirical CDS analysis, this paper applies the augmented Dickey–Fuller, Phillips–Perron, Kwiatkowski–Phillips–Schmidt–Shin, and Ng–Perron tests [...] Read more.
Credit default swap (CDS) spreads measure the default risk of the reference entity and have been frequently used in recent empirical papers. To provide a rigorous econometrics foundation for empirical CDS analysis, this paper applies the augmented Dickey–Fuller, Phillips–Perron, Kwiatkowski–Phillips–Schmidt–Shin, and Ng–Perron tests to study the unit root property of CDS spreads, and it uses the Phillips–Ouliaris–Hansen tests to determine whether they are cointegrated. The empirical sample consists of daily CDS spreads of the six large U.S. banks from 2001 to 2018. The main findings are that it is log, not raw, CDS spreads that are unit root processes, and that log CDS spreads are cointegrated. These findings imply that, even though the risks of individual banks may deviate from each other in the short run, there is a long-run relation that ties them together. As these CDS spreads are an important input for financial systemic risk, there are at least two policy implications. First, in monitoring systemic risk, policymakers should focus on long-run trends rather than short-run fluctuations of CDS spreads. Second, in controlling systemic risk, policy measures that reduce the long-run risks of individual banks, such as stress testing and capital buffers, are helpful in mitigating overall systemic risk. Full article
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18 pages, 675 KiB  
Article
Liquidity Risk Drivers and Bank Business Models
by Simona Galletta and Sebastiano Mazzù
Risks 2019, 7(3), 89; https://doi.org/10.3390/risks7030089 - 25 Aug 2019
Cited by 18 | Viewed by 9541
Abstract
This paper examines the bank liquidity risk while using a maturity mismatch indicator of loans and deposits (LTDm) during a specific period. Core banking activities that are based on the process of maturity transformation are the most exposed to liquidity risk. [...] Read more.
This paper examines the bank liquidity risk while using a maturity mismatch indicator of loans and deposits (LTDm) during a specific period. Core banking activities that are based on the process of maturity transformation are the most exposed to liquidity risk. The financial crisis in 2007–2009 highlighted the importance of liquidity to the functioning of both the financial markets and the banking sector. We investigate how characteristics of a bank, such as size, capital, and business model, are related to liquidity risk, while using a sample of European banks in the period after the financial crisis, from 2011 to 2017. While employing a generalized method of moment two-step estimator, we find that the banking size increases the liquidity risk, whereas capital is not an effective deterrent. Moreover, our findings reveal that, for savings banks, income diversification raises the liquidity risk while investment banks reliant on non-deposit funding decrease the exposure to liquidity risk. Full article
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15 pages, 1555 KiB  
Article
LIBOR Fallback and Quantitative Finance
by Marc Pierre Henrard
Risks 2019, 7(3), 88; https://doi.org/10.3390/risks7030088 - 15 Aug 2019
Cited by 8 | Viewed by 7401
Abstract
With the expected discontinuation of the LIBOR publication, a robust fallback for related financial instruments is paramount. In recent months, several consultations have taken place on the subject. The results of the first ISDA consultation have been published in November 2018 and a [...] Read more.
With the expected discontinuation of the LIBOR publication, a robust fallback for related financial instruments is paramount. In recent months, several consultations have taken place on the subject. The results of the first ISDA consultation have been published in November 2018 and a new one just finished at the time of writing. This note describes issues associated to the proposed approaches and potential alternative approaches in the framework and the context of quantitative finance. It evidences a clear lack of details and lack of measurability of the proposed approaches which would not be achievable in practice. It also describes the potential of asymmetrical information between market participants coming from the adjustment spread computation. In the opinion of this author, a fundamental revision of the fallback’s foundations is required. Full article
(This article belongs to the Special Issue Interest Rate Risk Modelling in Transformation)
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15 pages, 594 KiB  
Article
On the Laplace Transforms of the First Hitting Times for Drawdowns and Drawups of Diffusion-Type Processes
by Pavel V. Gapeev, Neofytos Rodosthenous and V. L. Raju Chinthalapati
Risks 2019, 7(3), 87; https://doi.org/10.3390/risks7030087 - 05 Aug 2019
Viewed by 3242
Abstract
We obtain closed-form expressions for the value of the joint Laplace transform of the running maximum and minimum of a diffusion-type process stopped at the first time at which the associated drawdown or drawup process hits a constant level before an independent exponential [...] Read more.
We obtain closed-form expressions for the value of the joint Laplace transform of the running maximum and minimum of a diffusion-type process stopped at the first time at which the associated drawdown or drawup process hits a constant level before an independent exponential random time. It is assumed that the coefficients of the diffusion-type process are regular functions of the current values of its running maximum and minimum. The proof is based on the solution to the equivalent inhomogeneous ordinary differential boundary-value problem and the application of the normal-reflection conditions for the value function at the edges of the state space of the resulting three-dimensional Markov process. The result is related to the computation of probability characteristics of the take-profit and stop-loss values of a market trader during a given time period. Full article
(This article belongs to the Special Issue Exit Problems for Lévy and Markov Processes with One-Sided Jumps and Related Topics)
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15 pages, 457 KiB  
Article
Optimal Risk Budgeting under a Finite Investment Horizon
by Marcos López de Prado, Ralph Vince and Qiji Jim Zhu
Risks 2019, 7(3), 86; https://doi.org/10.3390/risks7030086 - 05 Aug 2019
Cited by 4 | Viewed by 4527
Abstract
The Growth-Optimal Portfolio (GOP) theory determines the path of bet sizes that maximize long-term wealth. This multi-horizon goal makes it more appealing among practitioners than myopic approaches, like Markowitz’s mean-variance or risk parity. The GOP literature typically considers risk-neutral investors with an infinite [...] Read more.
The Growth-Optimal Portfolio (GOP) theory determines the path of bet sizes that maximize long-term wealth. This multi-horizon goal makes it more appealing among practitioners than myopic approaches, like Markowitz’s mean-variance or risk parity. The GOP literature typically considers risk-neutral investors with an infinite investment horizon. In this paper, we compute the optimal bet sizes in the more realistic setting of risk-averse investors with finite investment horizons. We find that, under this more realistic setting, the optimal bet sizes are considerably smaller than previously suggested by the GOP literature. We also develop quantitative methods for determining the risk-adjusted growth allocations (or risk budgeting) for a given finite investment horizon. Full article
(This article belongs to the Special Issue Portfolio Optimization and Risk Management: New Development and Applications)
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11 pages, 351 KiB  
Article
Potential Densities for Taxed Spectrally Negative Lévy Risk Processes
by Wenyuan Wang and Xiaowen Zhou
Risks 2019, 7(3), 85; https://doi.org/10.3390/risks7030085 - 02 Aug 2019
Cited by 1 | Viewed by 2261
Abstract
This paper revisits the spectrally negative Lévy risk process embedded with the general tax structure introduced in Kyprianou and Zhou (2009). A joint Laplace transform is found concerning the first down-crossing time below level 0. The potential density is also obtained for the [...] Read more.
This paper revisits the spectrally negative Lévy risk process embedded with the general tax structure introduced in Kyprianou and Zhou (2009). A joint Laplace transform is found concerning the first down-crossing time below level 0. The potential density is also obtained for the taxed Lévy risk process killed upon leaving [ 0 , b ] . The results are expressed using scale functions. Full article
(This article belongs to the Special Issue Exit Problems for Lévy and Markov Processes with One-Sided Jumps and Related Topics)
17 pages, 720 KiB  
Article
Parametric Conditions of High Financial Risk in the SME Sector
by Beata Ślusarczyk and Katarzyna Grondys
Risks 2019, 7(3), 84; https://doi.org/10.3390/risks7030084 - 01 Aug 2019
Cited by 15 | Viewed by 5685
Abstract
The sector of SME is the major force for the national economic and social development. Financial risk is one of the key threats to the activity of small and medium enterprises. The most common manifestation of the financial risk of SMEs is difficulty [...] Read more.
The sector of SME is the major force for the national economic and social development. Financial risk is one of the key threats to the activity of small and medium enterprises. The most common manifestation of the financial risk of SMEs is difficulty in financing the business and lack of funds for development. Banks are unwilling to grant loans to such companies. Moreover, it is the rising operating costs that cause shrinking profits, which may result in corporate debt, difficulty in debt repayment, and consequently, high financial risk of these entities. Numerous differences in conducting the activity of small and large enterprises intensify this risk and mean that the model of credit financing for companies is not adjusted to the capabilities and principles of the operation of small enterprises. Therefore, risk management is one of the most important internal processes in small and medium enterprises. The identification of factors that affect the level of financial risk in these entities is therefore crucial. The main objective of this research was to analyze the impact of selected parametric characteristics of the SME sector on the intensity of financial risk they take. This objective was accomplished on the basis of the survey with the participation of Polish SMEs. In order to test the adopted research assumptions, the linear regression model was used with four continuous variables for each type of the identified financial risk. Based on the final research results, the logit model was obtained for the risk of insufficient profits. It was indicated that both the internationalization of the company and the ability to manage risk are the only factors that affect a high level of risk of low income. The article ends with the discussion and the comparison with some previous research in this area. Full article
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21 pages, 389 KiB  
Article
Logarithmic Asymptotics for Probability of Component-Wise Ruin in a Two-Dimensional Brownian Model
by Krzysztof Dȩbicki, Lanpeng Ji and Tomasz Rolski
Risks 2019, 7(3), 83; https://doi.org/10.3390/risks7030083 - 01 Aug 2019
Cited by 2 | Viewed by 2402
Abstract
We consider a two-dimensional ruin problem where the surplus process of business lines is modelled by a two-dimensional correlated Brownian motion with drift. We study the ruin function P ( u ) for the component-wise ruin (that is both business lines are ruined [...] Read more.
We consider a two-dimensional ruin problem where the surplus process of business lines is modelled by a two-dimensional correlated Brownian motion with drift. We study the ruin function P ( u ) for the component-wise ruin (that is both business lines are ruined in an infinite-time horizon), where u is the same initial capital for each line. We measure the goodness of the business by analysing the adjustment coefficient, that is the limit of − ln P ( u ) / u as u tends to infinity, which depends essentially on the correlation ρ of the two surplus processes. In order to work out the adjustment coefficient we solve a two-layer optimization problem. Full article
(This article belongs to the Special Issue Exit Problems for Lévy and Markov Processes with One-Sided Jumps and Related Topics)
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18 pages, 1259 KiB  
Article
Loss Reserving Models: Granular and Machine Learning Forms
by Greg Taylor
Risks 2019, 7(3), 82; https://doi.org/10.3390/risks7030082 - 19 Jul 2019
Cited by 15 | Viewed by 4782
Abstract
The purpose of this paper is to survey recent developments in granular models and machine learning models for loss reserving, and to compare the two families with a view to assessment of their potential for future development. This is best understood against the [...] Read more.
The purpose of this paper is to survey recent developments in granular models and machine learning models for loss reserving, and to compare the two families with a view to assessment of their potential for future development. This is best understood against the context of the evolution of these models from their predecessors, and the early sections recount relevant archaeological vignettes from the history of loss reserving. However, the larger part of the paper is concerned with the granular models and machine learning models. Their relative merits are discussed, as are the factors governing the choice between them and the older, more primitive models. Concluding sections briefly consider the possible further development of these models in the future. Full article
(This article belongs to the Special Issue Claim Models: Granular Forms and Machine Learning Forms)
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24 pages, 1556 KiB  
Article
Hospital Proximity and Mortality in Australia
by Andrew Leung
Risks 2019, 7(3), 81; https://doi.org/10.3390/risks7030081 - 17 Jul 2019
Viewed by 2657
Abstract
It is intuitive that proximity to hospitals can only improve the chances of survival from a range of medical conditions. This study examines the empirical evidence for this assertion, based on Australian data. While hospital proximity might serve as a proxy for other [...] Read more.
It is intuitive that proximity to hospitals can only improve the chances of survival from a range of medical conditions. This study examines the empirical evidence for this assertion, based on Australian data. While hospital proximity might serve as a proxy for other factors, such as indigenity, income, wealth or geography, the evidence suggests that proximity provides the most direct link to these factors. In addition, as it turns out, a very statistically significant one that transcends economies. Full article
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11 pages, 1176 KiB  
Article
Quantile Regression with Telematics Information to Assess the Risk of Driving above the Posted Speed Limit
by Ana M. Pérez-Marín, Montserrat Guillen, Manuela Alcañiz and Lluís Bermúdez
Risks 2019, 7(3), 80; https://doi.org/10.3390/risks7030080 - 15 Jul 2019
Cited by 13 | Viewed by 3494
Abstract
We analyzed real telematics information for a sample of drivers with usage-based insurance policies. We examined the statistical distribution of distance driven above the posted speed limit—which presents a strong positive asymmetry—using quantile regression models. We found that, at different percentile levels, the [...] Read more.
We analyzed real telematics information for a sample of drivers with usage-based insurance policies. We examined the statistical distribution of distance driven above the posted speed limit—which presents a strong positive asymmetry—using quantile regression models. We found that, at different percentile levels, the distance driven at speeds above the posted limit depends on total distance driven and, more generally, on factors such as the percentage of urban and nighttime driving and on the driver’s gender. However, the impact of these covariates differs according to the percentile level. We stress the importance of understanding telematics information, which should not be limited to simply characterizing average drivers, but can be useful for signaling dangerous driving by predicting quantiles associated with specific driver characteristics. We conclude that the risk of driving for long distances above the speed limit is heterogeneous and, moreover, we show that prevention campaigns should target primarily male non-urban drivers, especially if they present a high percentage of nighttime driving. Full article
(This article belongs to the Special Issue Insurance: Spatial and Network Data)
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18 pages, 557 KiB  
Article
Individual Loss Reserving Using a Gradient Boosting-Based Approach
by Francis Duval and Mathieu Pigeon
Risks 2019, 7(3), 79; https://doi.org/10.3390/risks7030079 - 12 Jul 2019
Cited by 18 | Viewed by 5010
Abstract
In this paper, we propose models for non-life loss reserving combining traditional approaches such as Mack’s or generalized linear models and gradient boosting algorithm in an individual framework. These claim-level models use information about each of the payments made for each of the [...] Read more.
In this paper, we propose models for non-life loss reserving combining traditional approaches such as Mack’s or generalized linear models and gradient boosting algorithm in an individual framework. These claim-level models use information about each of the payments made for each of the claims in the portfolio, as well as characteristics of the insured. We provide an example based on a detailed dataset from a property and casualty insurance company. We contrast some traditional aggregate techniques, at the portfolio-level, with our individual-level approach and we discuss some points related to practical applications. Full article
(This article belongs to the Special Issue Claim Models: Granular Forms and Machine Learning Forms)
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20 pages, 3480 KiB  
Article
Market-Risk Optimization among the Developed and Emerging Markets with CVaR Measure and Copula Simulation
by Nader Trabelsi and Aviral Kumar Tiwari
Risks 2019, 7(3), 78; https://doi.org/10.3390/risks7030078 - 07 Jul 2019
Cited by 4 | Viewed by 3648
Abstract
In this paper, the generalized Pareto distribution (GPD) copula approach is utilized to solve the conditional value-at-risk (CVaR) portfolio problem. Particularly, this approach used (i) copula to model the complete linear and non-linear correlation dependence structure, (ii) Pareto tails to capture the estimates [...] Read more.
In this paper, the generalized Pareto distribution (GPD) copula approach is utilized to solve the conditional value-at-risk (CVaR) portfolio problem. Particularly, this approach used (i) copula to model the complete linear and non-linear correlation dependence structure, (ii) Pareto tails to capture the estimates of the parametric Pareto lower tail, the non-parametric kernel-smoothed interior and the parametric Pareto upper tail and (iii) Value-at-Risk (VaR) to quantify risk measure. The simulated sample covers the G7, BRICS (association of Brazil, Russia, India, China and South Africa) and 14 popular emerging stock-market returns for the period between 1997 and 2018. Our results suggest that the efficient frontier with the minimizing CVaR measure and simulated copula returns combined outperforms the risk/return of domestic portfolios, such as the US stock market. This result improves international diversification at the global level. We also show that the Gaussian and t-copula simulated returns give very similar but not identical results. Furthermore, the copula simulation provides more accurate market-risk estimates than historical simulation. Finally, the results support the notion that G7 countries can provide an important opportunity for diversification. These results are important to investors and policymakers. Full article
(This article belongs to the Special Issue Portfolio Optimization and Risk Management: New Development and Applications)
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15 pages, 434 KiB  
Article
Bankruptcy Risk, Its Financial Determinants and Reporting Delays: Do Managers Have Anything to Hide?
by Oliver Lukason and María-del-Mar Camacho-Miñano
Risks 2019, 7(3), 77; https://doi.org/10.3390/risks7030077 - 07 Jul 2019
Cited by 34 | Viewed by 5538
Abstract
The aim of this study was to investigate whether firms’ reporting delays are interconnected with bankruptcy risk and its financial determinants. This study was based on 698,189 firm-year observations from Estonia. Annual report submission delay, either in a binary or ordinal form, was [...] Read more.
The aim of this study was to investigate whether firms’ reporting delays are interconnected with bankruptcy risk and its financial determinants. This study was based on 698,189 firm-year observations from Estonia. Annual report submission delay, either in a binary or ordinal form, was used as the dependent variable, while bankruptcy risk based on an international model or the financial ratios determining it were the independent variables. The findings indicated that firms with lower values of liquidity and annual and accumulated profitability were more likely to delay the submission of an annual report over the legal deadline. In turn, firm leverage was not interconnected with reporting delays. In addition, firms with a higher risk of bankruptcy were more likely to delay the submission of their annual reports. Firms with different ages, sizes and industries varied in respect to the obtained results. Different stakeholders should be aware that when reporting delays occur, these can be conditioned by higher bankruptcy risk or poor performance, and thus, for instance, crediting such firms should be treated with caution. State institutions controlling timely submission should take strict(er) measures in cases of firms delaying for a lengthy period. Full article
21 pages, 1609 KiB  
Article
An Urn-Based Nonparametric Modeling of the Dependence between PD and LGD with an Application to Mortgages
by Dan Cheng and Pasquale Cirillo
Risks 2019, 7(3), 76; https://doi.org/10.3390/risks7030076 - 07 Jul 2019
Cited by 2 | Viewed by 4347
Abstract
We propose an alternative approach to the modeling of the positive dependence between the probability of default and the loss given default in a portfolio of exposures, using a bivariate urn process. The model combines the power of Bayesian nonparametrics and statistical learning, [...] Read more.
We propose an alternative approach to the modeling of the positive dependence between the probability of default and the loss given default in a portfolio of exposures, using a bivariate urn process. The model combines the power of Bayesian nonparametrics and statistical learning, allowing for the elicitation and the exploitation of experts’ judgements, and for the constant update of this information over time, every time new data are available. A real-world application on mortgages is described using the Single Family Loan-Level Dataset by Freddie Mac. Full article
(This article belongs to the Special Issue Advances in Credit Risk Modeling and Management)
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25 pages, 1758 KiB  
Article
The Time-Spatial Dimension of Eurozone Banking Systemic Risk
by Matteo Foglia and Eliana Angelini
Risks 2019, 7(3), 75; https://doi.org/10.3390/risks7030075 - 06 Jul 2019
Cited by 10 | Viewed by 4692
Abstract
In this paper, we measure the systemic risk with a novel methodology, based on a “spatial-temporal” approach. We propose a new bank systemic risk measure to consider the two components of systemic risk: cross-sectional and time dimension. The aim is to highlight the [...] Read more.
In this paper, we measure the systemic risk with a novel methodology, based on a “spatial-temporal” approach. We propose a new bank systemic risk measure to consider the two components of systemic risk: cross-sectional and time dimension. The aim is to highlight the “time-space dynamics” of contagion, i.e., if the CDS spread of bank i depends on the CDS spread of other banks. To do this, we use an advanced spatial econometrics design with a time-varying spatial dependence that can be interpreted as an index of the degree of cross-sectional spillovers. The findings highlight that the Eurozone banks have strong spatial dependence in the evolution of CDS spread, namely the contagion effect is present and persistent. Moreover, we analyse the role of the European Central Bank in managing contagion risk. We find that monetary policy has been effective in reducing systemic risk. However, the results show that systemic risk does not imply a policy intervention, highlighting how financial stability policy is not yet an objective. Full article
(This article belongs to the Special Issue Systemic Risk in Finance and Insurance)
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27 pages, 445 KiB  
Article
Can Machine Learning-Based Portfolios Outperform Traditional Risk-Based Portfolios? The Need to Account for Covariance Misspecification
by Prayut Jain and Shashi Jain
Risks 2019, 7(3), 74; https://doi.org/10.3390/risks7030074 - 03 Jul 2019
Cited by 20 | Viewed by 5930
Abstract
The Hierarchical risk parity (HRP) approach of portfolio allocation, introduced by Lopez de Prado (2016), applies graph theory and machine learning to build a diversified portfolio. Like the traditional risk-based allocation methods, HRP is also a function of the estimate of the covariance [...] Read more.
The Hierarchical risk parity (HRP) approach of portfolio allocation, introduced by Lopez de Prado (2016), applies graph theory and machine learning to build a diversified portfolio. Like the traditional risk-based allocation methods, HRP is also a function of the estimate of the covariance matrix, however, it does not require its invertibility. In this paper, we first study the impact of covariance misspecification on the performance of the different allocation methods. Next, we study under an appropriate covariance forecast model whether the machine learning based HRP outperforms the traditional risk-based portfolios. For our analysis, we use the test for superior predictive ability on out-of-sample portfolio performance, to determine whether the observed excess performance is significant or if it occurred by chance. We find that when the covariance estimates are crude, inverse volatility weighted portfolios are more robust, followed by the machine learning-based portfolios. Minimum variance and maximum diversification are most sensitive to covariance misspecification. HRP follows the middle ground; it is less sensitive to covariance misspecification when compared with minimum variance or maximum diversification portfolio, while it is not as robust as the inverse volatility weighed portfolio. We also study the impact of the different rebalancing horizon and how the portfolios compare against a market-capitalization weighted portfolio. Full article
(This article belongs to the Special Issue Modern Numerical Techniques and Machine-Learning in Pricing and Risk Management)
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11 pages, 348 KiB  
Article
De Finetti’s Control Problem with Parisian Ruin for Spectrally Negative Lévy Processes
by Jean-François Renaud
Risks 2019, 7(3), 73; https://doi.org/10.3390/risks7030073 - 03 Jul 2019
Cited by 6 | Viewed by 2355
Abstract
We consider de Finetti’s stochastic control problem when the (controlled) process is allowed to spend time under the critical level. More precisely, we consider a generalized version of this control problem in a spectrally negative Lévy model with exponential Parisian ruin. We show [...] Read more.
We consider de Finetti’s stochastic control problem when the (controlled) process is allowed to spend time under the critical level. More precisely, we consider a generalized version of this control problem in a spectrally negative Lévy model with exponential Parisian ruin. We show that, under mild assumptions on the Lévy measure, an optimal strategy is formed by a barrier strategy and that this optimal barrier level is always less than the optimal barrier level when classical ruin is implemented. In addition, we give necessary and sufficient conditions for the barrier strategy at level zero to be optimal. Full article
(This article belongs to the Special Issue Exit Problems for Lévy and Markov Processes with One-Sided Jumps and Related Topics)
29 pages, 1079 KiB  
Article
Premium Risk Net of Reinsurance: From Short-Term to Medium-Term Assessment
by Antonio Pallaria and Nino Savelli
Risks 2019, 7(3), 72; https://doi.org/10.3390/risks7030072 - 01 Jul 2019
Viewed by 4658
Abstract
Solvency II requirements introduced new issues for actuarial risk management in non-life insurance, challenging the market to have a consciousness of its own risk profile, and also investigating the sensitivity of the solvency ratio depending on the insurance risks and technical results on [...] Read more.
Solvency II requirements introduced new issues for actuarial risk management in non-life insurance, challenging the market to have a consciousness of its own risk profile, and also investigating the sensitivity of the solvency ratio depending on the insurance risks and technical results on either a short-term and medium-term perspective. For this aim, in the present paper, a partial internal model for premium risk is developed for three multi-line non-life insurers, and the impact of some different business mixes is analyzed. Furthermore, the risk-mitigation and profitability impact of reinsurance in the premium risk model are introduced, and a global framework for a feasible application of this model consistent with a medium-term analysis is provided. Numerical results are also figured out with evidence of various effects for several portfolios and reinsurance arrangements, pointing out the main reasons for these differences. Full article
(This article belongs to the Special Issue New Perspectives in Actuarial Risk Management)
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17 pages, 441 KiB  
Article
On the Validation of Claims with Excess Zeros in Liability Insurance: A Comparative Study
by Marjan Qazvini
Risks 2019, 7(3), 71; https://doi.org/10.3390/risks7030071 - 30 Jun 2019
Cited by 5 | Viewed by 3436
Abstract
In this study, we consider the problem of zero claims in a liability insurance portfolio and compare the predictability of three models. We use French motor third party liability (MTPL) insurance data, which has been used for a pricing game, and show that [...] Read more.
In this study, we consider the problem of zero claims in a liability insurance portfolio and compare the predictability of three models. We use French motor third party liability (MTPL) insurance data, which has been used for a pricing game, and show that how the type of coverage and policyholders’ willingness to subscribe to insurance pricing, based on telematics data, affects their driving behaviour and hence their claims. Using our validation set, we then predict the number of zero claims. Our results show that although a zero-inflated Poisson (ZIP) model performs better than a Poisson regression, it can even be outperformed by logistic regression. Full article
(This article belongs to the Special Issue Machine Learning in Insurance)
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