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

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...

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Bibliographic Details
Published in:Mathematics (Basel) 2023-02, Vol.11 (4), p.902
Main Authors: Zhong, Yangmin, Huang, Huaping
Format: Article
Language:English
Subjects:
Algorithms
Cash flow
Discount rates
Dividend policy
Dynamic programming
dynamic programming principle
Fixed point theory
Fixed points (mathematics)
Insurance
Insurance companies
Interest rates
Markov analysis
Markov chains
Mathematical models
Mathematical optimization
Numerical analysis
optimal dividend
Optimization
Random variables
Stockholders
Subsidies
Viscosity
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11040902