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Risks
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Loss Models: From Theory to Applications
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Loss Models: From Theory to Applications

A special issue of Risks (ISSN 2227-9091).

Deadline for manuscript submissions: closed (31 March 2020) | Viewed by 20535

Special Issue Editors

Prof. Dr. Jae Kyung Woo

E-Mail Website
Guest Editor
School of Risk and Actuarial Studies, University of New South Wales, Sydney 2052, Australia
Interests: risk theory; reliability theory; aggregate claim analysis; queueing theory; renewal processes
Dr. Eric Cheung

E-Mail Website
Guest Editor
School of Risk and Actuarial Studies, UNSW Business School, UNSW, Sydney, NSW 2052, Australia
Interests: insurance risk theory; ruin theory; aggregate claims analysis; credibility; financial mathematics; matrix-analytic methods; queueing theory; operations research; applied probability

Special Issue Information

Dear Colleagues,

The first edition of the textbook Loss Models: From Data to Decisions by Klugman, Panjer, and Willmot was published in 1998, and 2018 marks its 20th anniversary. The volume has expanded since 1998 to include more and more emerging important topics regarding loss modeling in actuarial science. The textbook is not only a required reading for various professional actuarial exams, but also a highly cited research reference as it contains a lot of classical results in actuarial science. The past 20 years have also seen the development of actuarial risk theory, along with the availability of more advanced statistical techniques, huge amount of data, and computational power.

 This Special Issue aims to collect state-of-the-art research papers tackling the latest challenges in theory and/or applications of loss models. While collective risk models are commonly used in general insurance and health insurance, they can also be utilized to model other types of risks, such as operational and credit risks. Due to the interdisciplinary nature of the subject, related models are often found in other areas, such as queueing theory, financial risk management, and statistics. Hence, the development of mathematical and stochastic models as well as statistical techniques could be employed in those disciplines. We warmly welcome papers related, but not limited to, the following topics:

  • Frequency/severity/compound distributions;
  • Risk/loss aggregation;
  • Ruin theory;
  • Credibility theory;
  • Reinsurance;
  • Dependence structure;
  • Extreme value theory;
  • Risk measures; and
  • Fitting and inference of loss models.
Prof. Jae Kyung Woo
Prof. Eric Cheung
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Risks is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Frequency/severity/compound distributions
  • Risk/loss aggregation
  • Ruin theory
  • Credibility theory
  • Reinsurance
  • Dependence structure
  • Extreme value theory
  • Risk measures
  • Fitting and inference of loss models

Published Papers (6 papers)

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Research

20 pages, 947 KiB  
Article
On Computations in Renewal Risk Models—Analytical and Statistical Aspects
by Josef Anton Strini and Stefan Thonhauser
Risks 2020, 8(1), 24; https://doi.org/10.3390/risks8010024 - 04 Mar 2020
Cited by 3 | Viewed by 2786
Abstract
We discuss aspects of numerical methods for the computation of Gerber-Shiu or discounted penalty-functions in renewal risk models. We take an analytical point of view and link this function to a partial-integro-differential equation and propose a numerical method for its solution. We show [...] Read more.
We discuss aspects of numerical methods for the computation of Gerber-Shiu or discounted penalty-functions in renewal risk models. We take an analytical point of view and link this function to a partial-integro-differential equation and propose a numerical method for its solution. We show weak convergence of an approximating sequence of piecewise-deterministic Markov processes (PDMPs) for deriving the convergence of the procedures. We will use estimated PDMP characteristics in a subsequent step from simulated sample data and study its effect on the numerically computed Gerber-Shiu functions. It can be seen that the main source of instability stems from the hazard rate estimator. Interestingly, results obtained using MC methods are hardly affected by estimation. Full article
(This article belongs to the Special Issue Loss Models: From Theory to Applications)
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26 pages, 1586 KiB  
Article
Loss Reserving Estimation With Correlated Run-Off Triangles in a Quantile Longitudinal Model
by Ioannis Badounas and Georgios Pitselis
Risks 2020, 8(1), 14; https://doi.org/10.3390/risks8010014 - 03 Feb 2020
Cited by 5 | Viewed by 3554
Abstract
In this paper, we consider a loss reserving model for a general insurance portfolio consisting of a number of correlated run-off triangles that can be embedded within the quantile regression model for longitudinal data. The model proposes a combination of the between- and [...] Read more.
In this paper, we consider a loss reserving model for a general insurance portfolio consisting of a number of correlated run-off triangles that can be embedded within the quantile regression model for longitudinal data. The model proposes a combination of the between- and within-subportfolios (run-off triangles) estimating functions for regression parameter estimation, which take into account the correlation and variation of the run-off triangles. The proposed method is robust to the error correlation structure, improves the efficiency of parameter estimators, and is useful for the estimation of the reserve risk margin and value at risk (VaR) in actuarial and finance applications. Full article
(This article belongs to the Special Issue Loss Models: From Theory to Applications)
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17 pages, 505 KiB  
Article
A New Heavy Tailed Class of Distributions Which Includes the Pareto
by Deepesh Bhati, Enrique Calderín-Ojeda and Mareeswaran Meenakshi
Risks 2019, 7(4), 99; https://doi.org/10.3390/risks7040099 - 20 Sep 2019
Cited by 10 | Viewed by 4012
Abstract
In this paper, a new heavy-tailed distribution, the mixture Pareto-loggamma distribution, derived through an exponential transformation of the generalized Lindley distribution is introduced. The resulting model is expressed as a convex sum of the classical Pareto and a special case of the loggamma [...] Read more.
In this paper, a new heavy-tailed distribution, the mixture Pareto-loggamma distribution, derived through an exponential transformation of the generalized Lindley distribution is introduced. The resulting model is expressed as a convex sum of the classical Pareto and a special case of the loggamma distribution. A comprehensive exploration of its statistical properties and theoretical results related to insurance are provided. Estimation is performed by using the method of log-moments and maximum likelihood. Also, as the modal value of this distribution is expressed in closed-form, composite parametric models are easily obtained by a mode matching procedure. The performance of both the mixture Pareto-loggamma distribution and composite models are tested by employing different claims datasets. Full article
(This article belongs to the Special Issue Loss Models: From Theory to Applications)
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16 pages, 407 KiB  
Article
Ruin Probability Functions and Severity of Ruin as a Statistical Decision Problem
by Emilio Gómez-Déniz, José María Sarabia and Enrique Calderín-Ojeda
Risks 2019, 7(2), 68; https://doi.org/10.3390/risks7020068 - 17 Jun 2019
Cited by 4 | Viewed by 3219
Abstract
It is known that the classical ruin function under exponential claim-size distribution depends on two parameters, which are referred to as the mean claim size and the relative security loading. These parameters are assumed to be unknown and random, thus, a loss function [...] Read more.
It is known that the classical ruin function under exponential claim-size distribution depends on two parameters, which are referred to as the mean claim size and the relative security loading. These parameters are assumed to be unknown and random, thus, a loss function that measures the loss sustained by a decision-maker who takes as valid a ruin function which is not correct can be considered. By using squared-error loss function and appropriate distribution function for these parameters, the issue of estimating the ruin function derives in a mixture procedure. Firstly, a bivariate distribution for mixing jointly the two parameters is considered, and second, different univariate distributions for mixing both parameters separately are examined. Consequently, a catalogue of ruin probability functions and severity of ruin, which are more flexible than the original one, are obtained. The methodology is also extended to the Pareto claim size distribution. Several numerical examples illustrate the performance of these functions. Full article
(This article belongs to the Special Issue Loss Models: From Theory to Applications)
22 pages, 484 KiB  
Article
Asymptotically Normal Estimators of the Ruin Probability for Lévy Insurance Surplus from Discrete Samples
by Yasutaka Shimizu and Zhimin Zhang
Risks 2019, 7(2), 37; https://doi.org/10.3390/risks7020037 - 03 Apr 2019
Cited by 9 | Viewed by 2604
Abstract
A statistical inference for ruin probability from a certain discrete sample of the surplus is discussed under a spectrally negative Lévy insurance risk. We consider the Laguerre series expansion of ruin probability, and provide an estimator for any of its partial sums by [...] Read more.
A statistical inference for ruin probability from a certain discrete sample of the surplus is discussed under a spectrally negative Lévy insurance risk. We consider the Laguerre series expansion of ruin probability, and provide an estimator for any of its partial sums by computing the coefficients of the expansion. We show that the proposed estimator is asymptotically normal and consistent with the optimal rate of convergence and estimable asymptotic variance. This estimator enables not only a point estimation of ruin probability but also an approximated interval estimation and testing hypothesis. Full article
(This article belongs to the Special Issue Loss Models: From Theory to Applications)
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15 pages, 474 KiB  
Article
A Genetic Algorithm for Investment–Consumption Optimization with Value-at-Risk Constraint and Information-Processing Cost
by Zhuo Jin, Zhixin Yang and Quan Yuan
Risks 2019, 7(1), 32; https://doi.org/10.3390/risks7010032 - 11 Mar 2019
Cited by 4 | Viewed by 3667
Abstract
This paper studies the optimal investment and consumption strategies in a two-asset model. A dynamic Value-at-Risk constraint is imposed to manage the wealth process. By using Value at Risk as the risk measure during the investment horizon, the decision maker can dynamically monitor [...] Read more.
This paper studies the optimal investment and consumption strategies in a two-asset model. A dynamic Value-at-Risk constraint is imposed to manage the wealth process. By using Value at Risk as the risk measure during the investment horizon, the decision maker can dynamically monitor the exposed risk and quantify the maximum expected loss over a finite horizon period at a given confidence level. In addition, the decision maker has to filter the key economic factors to make decisions. Considering the cost of filtering the factors, the decision maker aims to maximize the utility of consumption in a finite horizon. By using the Kalman filter, a partially observed system is converted to a completely observed one. However, due to the cost of information processing, the decision maker fails to process the information in an arbitrarily rational manner and can only make decisions on the basis of the limited observed signals. A genetic algorithm was developed to find the optimal investment, consumption strategies, and observation strength. Numerical simulation results are provided to illustrate the performance of the algorithm. Full article
(This article belongs to the Special Issue Loss Models: From Theory to Applications)
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