THE OPTIMAL DEDUCTIBLE AND COVERAGE IN INSURANCE CONTRACTS AND EQUILIBRIUM RISK SHARING POLICIES*

doi:10.1007/s10473-023-0320-3

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (3): 1347-1364.doi: 10.1007/s10473-023-0320-3

THE OPTIMAL DEDUCTIBLE AND COVERAGE IN INSURANCE CONTRACTS AND EQUILIBRIUM RISK SHARING POLICIES^*

Lingling Jian

School of Mathematical Sciences, Nankai University, Tianjin 300071, China

收稿日期:2021-09-14 修回日期:2022-01-27 出版日期:2023-06-25 发布日期:2023-06-06
作者简介:Lingling Jian, E-mail: janejzh@163.com
基金资助:
NSF of China (11931018, 12271274) and the Tianjin Natural Science Foundation (19JCYBJC30400).

THE OPTIMAL DEDUCTIBLE AND COVERAGE IN INSURANCE CONTRACTS AND EQUILIBRIUM RISK SHARING POLICIES^*

Lingling Jian

School of Mathematical Sciences, Nankai University, Tianjin 300071, China

Received:2021-09-14 Revised:2022-01-27 Online:2023-06-25 Published:2023-06-06
About author:Lingling Jian, E-mail: janejzh@163.com
Supported by:
NSF of China (11931018, 12271274) and the Tianjin Natural Science Foundation (19JCYBJC30400).

摘要/Abstract

摘要： In this paper, we consider the optimal risk sharing problem between two parties in the insurance business: the insurer and the insured. The risk is allocated between the insurer and the insured by setting a deductible and coverage in the insurance contract. We obtain the optimal deductible and coverage by considering the expected product of the two parties' utilities of terminal wealth according to stochastic optimal control theory. An equilibrium policy is also derived for when there are both a deductible and coverage; this is done by modelling the problem as a stochastic game in a continuous-time framework. A numerical example is provided to illustrate the results of the paper.

关键词: deductible and coverage, equilibrium policy, stochastic optimal control, Hamilton-Jacobi-Bellman equation

Abstract: In this paper, we consider the optimal risk sharing problem between two parties in the insurance business: the insurer and the insured. The risk is allocated between the insurer and the insured by setting a deductible and coverage in the insurance contract. We obtain the optimal deductible and coverage by considering the expected product of the two parties' utilities of terminal wealth according to stochastic optimal control theory. An equilibrium policy is also derived for when there are both a deductible and coverage; this is done by modelling the problem as a stochastic game in a continuous-time framework. A numerical example is provided to illustrate the results of the paper.

Key words: deductible and coverage, equilibrium policy, stochastic optimal control, Hamilton-Jacobi-Bellman equation

Lingling Jian. THE OPTIMAL DEDUCTIBLE AND COVERAGE IN INSURANCE CONTRACTS AND EQUILIBRIUM RISK SHARING POLICIES^*[J]. 数学物理学报(英文版), 2023, 43(3): 1347-1364.

Lingling Jian. THE OPTIMAL DEDUCTIBLE AND COVERAGE IN INSURANCE CONTRACTS AND EQUILIBRIUM RISK SHARING POLICIES^*[J]. Acta mathematica scientia,Series B, 2023, 43(3): 1347-1364.

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THE OPTIMAL DEDUCTIBLE AND COVERAGE IN INSURANCE CONTRACTS AND EQUILIBRIUM RISK SHARING POLICIES^*

THE OPTIMAL DEDUCTIBLE AND COVERAGE IN INSURANCE CONTRACTS AND EQUILIBRIUM RISK SHARING POLICIES^*

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