Reinsurance Policy under Interest Force and Bankruptcy Prohibition

In this paper, we solve an optimal reinsurance problem in the mathematical finance area. We assume that the surplus process of the insurance company follows a controlled diffusion process and the constant interest rate is involved in the financial model. During the whole optimization period, the com...

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Bibliographic Details
Published in:Axioms 2023-04, Vol.12 (4), p.378
Main Authors: Zhong, Yangmin, Huang, Huaping
Format: Article
Language:English
Subjects:
Actuarial science
Bankruptcy
Boundary conditions
Central banks
Control theory
Diffusion rate
dual transformation
dynamic programming principle
Expected utility
Hamilton-Jacobi-Bellman equation
Insurance companies
Interest rates
Investments
Laws, regulations and rules
Mathematical analysis
Mathematical optimization
Methods
Optimal control
Optimization
Partial differential equations
Prohibition
Reinsurance
Securities markets
Stochastic control theory
stochastic optimal control
Stochastic processes
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Summary:In this paper, we solve an optimal reinsurance problem in the mathematical finance area. We assume that the surplus process of the insurance company follows a controlled diffusion process and the constant interest rate is involved in the financial model. During the whole optimization period, the company has a choice to buy reinsurance contract and decide the reinsurance retention level. Meanwhile, the bankruptcy at the terminal time is not allowed. The aim of the optimization problem is to minimize the distance between the terminal wealth and a given goal by controlling the reinsurance proportion. Using the stochastic control theory, we derive the Hamilton-Jacobi-Bellman equation for the optimization problem. Via adopting the technique of changing variable as well as the dual transformation, an explicit solution of the value function and the optimal policy are shown. Finally, several numerical examples are shown, from which we find several main factors that affect the optimal reinsurance policy.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms12040378