Abstract
In this paper, we consider the problem of maximizing the expected discounted utility of dividend payments for an insurance company taking into account the time value of ruin. We assume the preference of the insurer is of the CRRA form. The discounting factor is modeled as a geometric Brownian motion. We introduce the VaR control levels for the insurer to control its loss in reinsurance strategies. By solving the corresponding Hamilton-Jacobi-Bellman equation, we obtain the value function and the corresponding optimal strategy. Finally, we provide some numerical examples to illustrate the results and analyze the VaR control levels on the optimal strategy.
Highlights
In recent years, dividend optimization problems for insurance company have attracted extensive attention
Many interesting results have been obtained under reinsurance strategy in recent years
For example, Azcue and Muler [14], who studied the optimal reinsurance in the framework of Cramér-Lundberg model
Summary
Dividend optimization problems for insurance company have attracted extensive attention. The problem of optimal dividend was proposed by De Finetti in 1957 He suggested that a company would seek to find a strategy in order to maximize the accumulated value of expected discounted dividends up to the ruin time. Chen et al [21] investigated the optimal reinsurance strategies and the minimum probability of ruin with VaR constraints. We are going to study the problem of maximizing the expected discounted utility of dividend, taking into account both reinsurance under VaR constraints and a stochastic interest rate. By solving the corresponding Hamilton-JacobiBellman equation, we obtain the value function and the corresponding optimal strategies with and without VaR constraints.
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