二维对偶模型的最优分红

Optimal Dividend in the Two-Dimensional Dual Model

研究阈值分红策略下带扩散的二维对偶模型,得到分红现值的期望所满足的积分微分方程组,并用此方程组解得收入服从指数分布时的分红折现的期望具体表达式,应用拉普拉斯变换求得收益服从任意分布时的解,最后解得了此模型下的最优边界。

We study the two-dimensional dual model with diffusion under a threshold dividend strategy. We obtain a group of integro-differential equations satisfied by the expected total sum of discount dividends until ruin. And explicit results when the gains of the two projects are exponentially distributed are derived. By applying the method of the Laplace transform, we solve the case where gains follow general distributions. We also illustrate how to calculate the optimal dividend threshold.