{"title":"Gambler's ruin problem in a Markov-modulated jump-diffusion risk model","authors":"Yuxuan Liu, Zhengjun Jiang, Yixin Qu","doi":"10.1080/03461238.2021.2025145","DOIUrl":null,"url":null,"abstract":"ABSTRACT When an insurance company's risk reserve is governed by a Markov-modulated jump-diffusion risk model, we study gambler's ruin problem in terms of two-sided ruin probability that the insurance company shall be ruined before its risk reserve reaches an upper barrier level . We employ Banach contraction principle and q-scale functions to confirm the two-sided ruin probability to be the only fixed point of a contraction mapping and construct an iterative algorithm of approximating the two-sided ruin probability. We find that the two-sided ruin probability and Lipschitz constant in the contraction mapping depend on the upper barrier level b, premium rate per squared volatility, Markov intensity rate per squared volatility, Poisson intensity rate per squared volatility and the mean value of claim per unit of time. Finally, we present a numerical example with two regimes to show the efficiency of the iterative algorithm.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2022-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Scandinavian Actuarial Journal","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.1080/03461238.2021.2025145","RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
ABSTRACT When an insurance company's risk reserve is governed by a Markov-modulated jump-diffusion risk model, we study gambler's ruin problem in terms of two-sided ruin probability that the insurance company shall be ruined before its risk reserve reaches an upper barrier level . We employ Banach contraction principle and q-scale functions to confirm the two-sided ruin probability to be the only fixed point of a contraction mapping and construct an iterative algorithm of approximating the two-sided ruin probability. We find that the two-sided ruin probability and Lipschitz constant in the contraction mapping depend on the upper barrier level b, premium rate per squared volatility, Markov intensity rate per squared volatility, Poisson intensity rate per squared volatility and the mean value of claim per unit of time. Finally, we present a numerical example with two regimes to show the efficiency of the iterative algorithm.
期刊介绍：
Scandinavian Actuarial Journal is a journal for actuarial sciences that deals, in theory and application, with mathematical methods for insurance and related matters.
The bounds of actuarial mathematics are determined by the area of application rather than by uniformity of methods and techniques. Therefore, a paper of interest to Scandinavian Actuarial Journal may have its theoretical basis in probability theory, statistics, operations research, numerical analysis, computer science, demography, mathematical economics, or any other area of applied mathematics; the main criterion is that the paper should be of specific relevance to actuarial applications.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
