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Cash Flow Optimization on Insurance: An Application of Fixed-Point Theory

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Listed:
  • Yangmin Zhong

    (School of Law, Shanghai University of Finance and Economics, Shanghai 200433, China)

  • Huaping Huang

    (School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, Chongqing 404020, China)

Abstract

The purpose of this paper is to explore a discrete-time cash flow optimization problem of the insurance company with time value of ruin under different interest rates. For the sake of considering the time value of ruin, we assume that the shareholders can get subsidies per unit time, as long as the insurance company is not bankrupt. The switching of different interest rates on the market is controlled by a stationary Markov chain. The dynamic programming principle is used to solve this optimization problem. By using the method of fixed-point theory, we show that the value function is the unique solution of the dynamic programming equation and a numerical algorithm is proposed to solve the value function as well as the optimal policy. Furthermore, two examples are revealed to illustrate the application of the main results obtained in the presented paper.

Suggested Citation

  • Yangmin Zhong & Huaping Huang, 2023. "Cash Flow Optimization on Insurance: An Application of Fixed-Point Theory," Mathematics, MDPI, vol. 11(4), pages 1-12, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:902-:d:1064304
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    References listed on IDEAS

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