Computing two actuarial quantities under multilayer dividend strategy with a constant interest rate: Based on Sinc methods

IF 3.4 2区 数学 Q1 MATHEMATICS, APPLIED
Zhang Liu, Sijia Shen, Haipeng Su
{"title":"Computing two actuarial quantities under multilayer dividend strategy with a constant interest rate: Based on Sinc methods","authors":"Zhang Liu,&nbsp;Sijia Shen,&nbsp;Haipeng Su","doi":"10.1016/j.cnsns.2024.108369","DOIUrl":null,"url":null,"abstract":"<div><div>As risk processes with some kind of dividend strategies receive remarkable attention in the financial market, the analysis of risk quantities in the presence of interest (or return) has become an important issue in insurance risk theory, and the corresponding research should be of concern to actuaries. In this paper, we study a perturbed dual risk model with a constant interest rate and a multilayer threshold strategy. We derive respectively the integral differential equations satisfied by the expected present value of the total dividend until ruin and the Laplace transform at the time of ruin. By applying the Sinc method developed in this paper, we derive the approximate solutions of the integral differential equations satisfied by these two risk quantities. Finally, various numerical examples are provided to demonstrate the feasibility of the Sinc method.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4000,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Nonlinear Science and Numerical Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1007570424005549","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0

Abstract

As risk processes with some kind of dividend strategies receive remarkable attention in the financial market, the analysis of risk quantities in the presence of interest (or return) has become an important issue in insurance risk theory, and the corresponding research should be of concern to actuaries. In this paper, we study a perturbed dual risk model with a constant interest rate and a multilayer threshold strategy. We derive respectively the integral differential equations satisfied by the expected present value of the total dividend until ruin and the Laplace transform at the time of ruin. By applying the Sinc method developed in this paper, we derive the approximate solutions of the integral differential equations satisfied by these two risk quantities. Finally, various numerical examples are provided to demonstrate the feasibility of the Sinc method.
计算恒定利率多层分红策略下的两个精算量:基于 Sinc 方法
随着带有某种分红策略的风险过程在金融市场上受到广泛关注,对存在利息(或回报)的风险量的分析已成为保险风险理论中的一个重要问题,相应的研究也应引起精算师的关注。本文研究了一个具有恒定利率和多层阈值策略的扰动双重风险模型。我们分别推导了毁损前总红利的期望现值和毁损时的拉普拉斯变换所满足的积分微分方程。通过应用本文开发的 Sinc 方法,我们得出了这两个风险量所满足的积分微分方程的近似解。最后,我们提供了各种数值示例来证明 Sinc 方法的可行性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Communications in Nonlinear Science and Numerical Simulation
Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
CiteScore
6.80
自引率
7.70%
发文量
378
审稿时长
78 days
期刊介绍: The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信