相关双边跳扩散模型的期望折现罚金函数

Expected Discounted Function Under a Correlated Two-sided Jump-diffusion Model

带干扰的经典风险模型,其干扰项可被解释为未来的总理赔量,保费收入以及未来投资收益的不确定性,用双指数跳扩散过程来描述这些不确定性,考虑双边跳扩散模型的期望折现罚金函数,给出其所满足的积分微分方程,并给出破产时间和破产时公司现值的联合拉普拉斯变换的显式表达公式.

In the perturbed classical risk model, the perturbed part is usually interprieted as the fluctuation of the total claim amount, the premium income and the surplus investment return. This paper uses a double expontial jump diffusion model to describle the fluctuation. We consider the expected discounted penalty function under a correlated two-sided jump diffussion model, and deduce the integro-differential equation satisfied by it. We also give the explicit expression for the joint Laplace transform of the ruin time and the firm value.