Stochastic Interest Model Based on Compound Poisson Process and Applications in Actuarial Science

Author:

Li Shilong12,Yin Chuancun1ORCID,Zhao Xia3ORCID,Dai Hongshuai4

Affiliation:

1. School of Statistics, Qufu Normal University, Qufu, Shandong 273165, China

2. School of Insurance, Shandong University of Finance and Economics, Jinan, Shandong 250014, China

3. School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai 201620, China

4. School of Statistics, Shandong University of Finance and Economics, Jinan, Shandong 250014, China

Abstract

Considering stochastic behavior of interest rates in financial market, we construct a new class of interest models based on compound Poisson process. Different from the references, this paper describes the randomness of interest rates by modeling the force of interest with Poisson random jumps directly. To solve the problem in calculation of accumulated interest force function, one important integral technique is employed. And a conception called the critical value is introduced to investigate the validity condition of this new model. We also discuss actuarial present values of several life annuities under this new interest model. Simulations are done to illustrate the theoretical results and the effect of parameters in interest model on actuarial present values is also analyzed.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. The Bell–Touchard counting process;Applied Mathematics and Computation;2023-05

2. Web renewal counting processes and their applications in insurance;Journal of Inequalities and Applications;2018-09-25

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