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Risks
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Interplay between Financial and Actuarial Mathematics II
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Interplay between Financial and Actuarial Mathematics II

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

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 11845

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 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

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

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Published Papers (7 papers)

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Editorial

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2 pages, 229 KiB  
Editorial
Special Issue “Interplay Between Financial and Actuarial Mathematics II”
by Corina Constantinescu and Julia Eisenberg
Risks 2024, 12(11), 177; https://doi.org/10.3390/risks12110177 - 8 Nov 2024
Viewed by 342
Abstract
Dear Reader, [...] Full article
(This article belongs to the Special Issue Interplay between Financial and Actuarial Mathematics II)

Research

Jump to: Editorial

15 pages, 492 KiB  
Article
Bounds for the Ruin Probability in the Sparre–Andersen Model
by Sotirios Losidis and Vaios Dermitzakis
Risks 2024, 12(2), 28; https://doi.org/10.3390/risks12020028 - 2 Feb 2024
Viewed by 1671
Abstract
We obtain the upper and lower bounds for the ruin probability in the Sparre–Andersen model. These bounds are established under various conditions: when the adjustment coefficient exists, when it does not exist, and when the interarrival distribution belongs to certain aging classes. Additionally, [...] Read more.
We obtain the upper and lower bounds for the ruin probability in the Sparre–Andersen model. These bounds are established under various conditions: when the adjustment coefficient exists, when it does not exist, and when the interarrival distribution belongs to certain aging classes. Additionally, we improve the Lundberg upper bound for the ruin probability. Full article
(This article belongs to the Special Issue Interplay between Financial and Actuarial Mathematics II)
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26 pages, 769 KiB  
Article
Maximum Pseudo-Likelihood Estimation of Copula Models and Moments of Order Statistics
by Alexandra Dias
Risks 2024, 12(1), 15; https://doi.org/10.3390/risks12010015 - 18 Jan 2024
Viewed by 2036
Abstract
It has been shown that, despite being consistent and in some cases efficient, maximum pseudo-likelihood (MPL) estimation for copula models overestimates the level of dependence, especially for small samples with a low level of dependence. This is especially relevant in finance and insurance [...] Read more.
It has been shown that, despite being consistent and in some cases efficient, maximum pseudo-likelihood (MPL) estimation for copula models overestimates the level of dependence, especially for small samples with a low level of dependence. This is especially relevant in finance and insurance applications when data are scarce. We show that the canonical MPL method uses the mean of order statistics, and we propose to use the median or the mode instead. We show that the MPL estimators proposed are consistent and asymptotically normal. In a simulation study, we compare the finite sample performance of the proposed estimators with that of the original MPL and the inversion method estimators based on Kendall’s tau and Spearman’s rho. In our results, the modified MPL estimators, especially the one based on the mode of the order statistics, have a better finite sample performance both in terms of bias and mean square error. An application to general insurance data shows that the level of dependence estimated between different products can vary substantially with the estimation method used. Full article
(This article belongs to the Special Issue Interplay between Financial and Actuarial Mathematics II)
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14 pages, 417 KiB  
Article
Some Stochastic Orders over an Interval with Applications
by Lazaros Kanellopoulos
Risks 2023, 11(9), 161; https://doi.org/10.3390/risks11090161 - 5 Sep 2023
Viewed by 1810
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)
16 pages, 632 KiB  
Article
Asymptotic 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 1634
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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15 pages, 934 KiB  
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 - 9 Mar 2023
Viewed by 1491
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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21 pages, 473 KiB  
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
Cited by 1 | Viewed by 1677
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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