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.

中文翻译：

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VaR约束和随机利率下具有比例再保险的股息支付的最优预期效用

在本文中，考虑到破产的时间价值，我们考虑使保险公司的股息支付的预期折现效用最大化的问题。我们假设保险公司的偏好是CRRA形式。折现因子建模为几何布朗运动。我们为保险公司介绍了VaR控制级别，以控制其在再保险策略中的损失。通过求解相应的Hamilton-Jacobi-Bellman方程，我们获得了价值函数和相应的最优策略。最后，我们提供一些数值示例来说明结果，并在最优策略上分析VaR控制级别。