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Risks
Special Issues
Interplay between Financial and Actuarial Mathematics II
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Special Issue "Interplay between Financial and Actuarial Mathematics II"

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

Deadline for manuscript submissions: 31 December 2023 | Viewed by 6833

Special Issue Editors

Prof. Dr. Corina Constantinescu

E-Mail Website
Guest Editor
Institute for Financial and Actuarial Mathematics, Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK
Interests: actuarial science; risk theory; dependence structures; heavy-tailed distributions; bonus-malus systems
Special Issues, Collections and Topics in MDPI journals
Dr. Julia Eisenberg

E-Mail Website
Guest Editor
Financial & Actuarial Mathematics, Vienna University of Technology, Wiedner Hauptstr. 8/E105-1, 1040 Vienna, Austria
Interests: actuarial mathematics; stochastic optimization; optimal control theory; reinsurance, dividends, capital injections in insurance companies; optimal consumption
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Due to the lasting ultra-low interest rate environment, the interplay between actuarial and financial mathematics along with the control theory have become a focus of interest for both researchers and practitioners. Many emerging insurance products involve financial instruments and vice versa. Therefore, being aware of the methods applied in both branches presents novel perspectives and could help solve topical problems.

In this Special Issue, we welcome high-quality research papers highlighting the interaction between actuarial and financial mathematics. You are cordially invited to submit your research on actuarial problems involving financial instruments; stochastic optimal control in insurance; and innovative risk measures involving both actuarial and financial elements.

This Special Issue is a continuation of the previous successful Special Issue “Interplay between Financial and Actuarial Mathematics".

Prof. Dr. Corina Constantinescu
Dr. Julia Eisenberg
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 1400 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

  • insurance mathematics
  • financial mathematics
  • point processes
  • Monte Carlo simulation
  • risk analysis

Published Papers (6 papers)

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Article
Some Stochastic Orders over an Interval with Applications
by
Lazaros Kanellopoulos
Risks 2023, 11(9), 161; https://doi.org/10.3390/risks11090161 - 05 Sep 2023
Viewed by 791
Abstract
In this article, we study stochastic orders over an interval. Mainly, we focus on orders related to the Laplace transform. The results are then applied to obtain a bound for heavy-tailed distributions and are illustrated by some examples. We also indicate how these [...] Read more.
In this article, we study stochastic orders over an interval. Mainly, we focus on orders related to the Laplace transform. The results are then applied to obtain a bound for heavy-tailed distributions and are illustrated by some examples. We also indicate how these ordering relationships can be adapted to the classical risk model in order to derive a moment bound for ruin probability. Finally, we compare it with other existing bounds. Full article
(This article belongs to the Special Issue Interplay between Financial and Actuarial Mathematics II)
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Article
Asymptototic Expected Utility of Dividend Payments in a Classical Collective Risk Process
by
Sebastian Baran
,
Corina Constantinescu
and
Zbigniew Palmowski
Risks 2023, 11(4), 64; https://doi.org/10.3390/risks11040064 - 23 Mar 2023
Viewed by 819
Abstract
We find the asymptotics of the value function maximizing the expected utility of discounted dividend payments of an insurance company whose reserves are modeled as a classical Cramér risk process, with exponentially distributed claims, when the initial reserves tend to infinity. We focus [...] Read more.
We find the asymptotics of the value function maximizing the expected utility of discounted dividend payments of an insurance company whose reserves are modeled as a classical Cramér risk process, with exponentially distributed claims, when the initial reserves tend to infinity. We focus on the power and logarithmic utility functions. We also perform some numerical analysis. Full article
(This article belongs to the Special Issue Interplay between Financial and Actuarial Mathematics II)
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Article
A Note on a Modified Parisian Ruin Concept
by
Eric C. K. Cheung
and
Jeff T. Y. Wong
Risks 2023, 11(3), 56; https://doi.org/10.3390/risks11030056 - 09 Mar 2023
Viewed by 667
Abstract
Traditionally, Parisian ruin is said to occur when the insurer’s surplus process has stayed below level zero continuously for a certain grace period. Inspired by this concept, in this paper we propose a modification by assuming that once a grace period has been [...] Read more.
Traditionally, Parisian ruin is said to occur when the insurer’s surplus process has stayed below level zero continuously for a certain grace period. Inspired by this concept, in this paper we propose a modification by assuming that once a grace period has been granted when the surplus becomes negative, the surplus level will not be monitored continuously in the interim, but instead it will be checked at the end of the grace period to see whether the business has recovered. Under an Erlang distributed grace period, a computationally tractable formula for the Gerber–Shiu expected discounted penalty function is derived. Numerical examples regarding the modified Parisian ruin probability are also provided. Full article
(This article belongs to the Special Issue Interplay between Financial and Actuarial Mathematics II)
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Article
Dependence Modelling of Lifetimes in Egyptian Families
by
Kira Henshaw
,
Waleed Hana
,
Corina Constantinescu
and
Dalia Khalil
Risks 2023, 11(1), 18; https://doi.org/10.3390/risks11010018 - 11 Jan 2023
Viewed by 1512
Abstract
In this study, we analyse a large sample of Egyptian social pension data which covers, by law, the policyholder’s spouse, children, parents and siblings. This data set uniquely enables the study and comparison of pairwise dependence between multiple familial relationships beyond the well-known [...] Read more.
In this study, we analyse a large sample of Egyptian social pension data which covers, by law, the policyholder’s spouse, children, parents and siblings. This data set uniquely enables the study and comparison of pairwise dependence between multiple familial relationships beyond the well-known husband and wife case. Applying Bayesian Markov Chain Monte Carlo (MCMC) estimation techniques with the two-step inference functions for margins (IFM) method, we model dependence between lifetimes in spousal, parent–child and child–parent relationships, using copulas to capture the strength of association. Dependence is observed to be strongest in child–parent relationships and, in comparison to the high-income countries of data sets previously studied, of lesser significance in the husband and wife case, often referred to as broken-heart syndrome. Given the traditional use of UK mortality tables in the modelling of mortality in Egypt, the findings of this paper will help to inform appropriate mortality assumptions specific to the unique structure of the Egyptian scheme. Full article
(This article belongs to the Special Issue Interplay between Financial and Actuarial Mathematics II)
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Article
Recursive Approaches for Multi-Layer Dividend Strategies in a Phase-Type Renewal Risk Model
by
Apostolos D. Papaioannou
and
Lewis Ramsden
Risks 2023, 11(1), 1; https://doi.org/10.3390/risks11010001 - 20 Dec 2022
Viewed by 854
Abstract
In this paper we consider a risk model with two independent classes of insurance risks in the presence of a multi-layer dividend strategy. We assume that both of the claim number processes are renewal processes with phase-type inter-arrival times. By analysing the Markov [...] Read more.
In this paper we consider a risk model with two independent classes of insurance risks in the presence of a multi-layer dividend strategy. We assume that both of the claim number processes are renewal processes with phase-type inter-arrival times. By analysing the Markov chains associated with the two given phase-type distributions of the inter-arrival times, algorithmic schemes for the determination of explicit expressions for the Gerber–Shiu expected discounted penalty function, as well as the expected discounted dividend payments are derived, using two different approaches. Full article
(This article belongs to the Special Issue Interplay between Financial and Actuarial Mathematics II)
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Article
Effect of Stop-Loss Reinsurance on Primary Insurer Solvency
by
Corina Constantinescu
,
Alexandra Dias
,
Bo Li
,
David Šiška
and
Simon Wang
Risks 2022, 10(10), 193; https://doi.org/10.3390/risks10100193 - 10 Oct 2022
Viewed by 1520
Abstract
Stop-loss reinsurance is a risk management tool that allows an insurance company to transfer part of their risk to a reinsurance company. Ruin probabilities allow us to measure the effect of stop-loss reinsurance on the solvency of the primary insurer. They further permit [...] Read more.
Stop-loss reinsurance is a risk management tool that allows an insurance company to transfer part of their risk to a reinsurance company. Ruin probabilities allow us to measure the effect of stop-loss reinsurance on the solvency of the primary insurer. They further permit the calculation of the economic capital, or the required initial capital to hold, corresponding to the 99.5% value-at-risk of its surplus. Specifically, we show that under a stop-loss contract, the ruin probability for the primary insurer, for both a finite- and infinite-time horizon, can be obtained from the finite-time ruin probability when no reinsurance is bought. We develop a finite-difference method for solving the (partial integro-differential) equation satisfied by the finite-time ruin probability with no reinsurance, leading to numerical approximations of the ruin probabilities under a stop-loss reinsurance contract. Using the method developed here, we discuss the interplay between ruin probability, reinsurance retention level and initial capital. Full article
(This article belongs to the Special Issue Interplay between Financial and Actuarial Mathematics II)
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