阈红利策略下带有扰动的对偶风险模型的最优红利

研究了阈红利策略下的对偶风险模型,其公司盈余是一个样本路径满足向下免跳的Lévy过程,总收入过程是一个可改变的复合泊松过程与一个独立的维纳过程之和.获得了直到破产为止的红利折现期望值V(u;b)满足的一组可积微分方程,利用其中一个可积微分方程即可得到V(u;b),在利润额服从混合指数分布的情形下求解了V(u;b).用拉普拉斯变换得到了V(u;b),并说明最优红利边界的获得方法.

Optimal Dividends in the Perturbed Dual Model with A Threshold Dividend Strategy

The dual model with a dividend threshold is studied. In the model, the surplus of a company is a Levy process with sample paths that are skip-free downwards, the aggregate gains process is the sum of a shifted compound Poisson process and an independent Wiener process. A set of integral and differential equations satisfied by the expected total discounted dividends V（u;b） until ruin are derived and V（u;b） can be solved by using only one of the integral and differential equations. The cases where profits follow a mix ture of exponential distributions is then solved and the discussion for the cases of a general profit distribution follows by the use of Laplace transforms. It is illustrated that how to obtain the optimal threshold level that maximizes the expected total discounted dividends until ruin.