In this paper we assume the insurance wealth process is driven by the compound Poisson process. The discounting factor is modelled as a geometric Brownian motion at first and then as an exponential function of an integrated Ornstein-Uhlenbeck process. The objective is to maximize the cumulated value of expected discounted dividends up to the time of ruin. We give an explicit expression of the value function and the optimal strategy in the case of interest rate following a geometric Brownian motion. For the case of the Vasicek model, we explore some properties of the value function. Since we can not find an explicit expression for the value function in the second case, we prove that the value function is the viscosity solution of the corresponding HJB equation.

中文翻译：

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随机利率下复合泊松过程的最优分红

在本文中，我们假设保险财富过程是由复合泊松过程驱动的。首先将折现因子建模为几何布朗运动，然后建模为集成的Ornstein-Uhlenbeck过程的指数函数。目的是在破产之前最大程度地提高预期折现股息的累计价值。在几何布朗运动之后的利率情况下，我们给出了价值函数和最优策略的明确表示。对于Vasicek模型，我们探讨了值函数的一些属性。由于在第二种情况下我们找不到值函数的显式表达式，因此我们证明了值函数是相应HJB方程的粘度解。