{"title":"Computing two actuarial quantities under multilayer dividend strategy with a constant interest rate: Based on Sinc methods","authors":"Zhang Liu, Sijia Shen, 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.
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.