一个破产时罚金折现期望的更新方程

A Renewal Equation for Expected Discounted Penalty at Ruin

考虑经典风险模型下带有一种随机利率的破产时罚金折现期望,其利率的随机性通过标准Wiener过程和Poisson过程来描述.就这种随机利率的情形,给出破产时罚金折现期望满足的积分-微分方程和更新方程.

In the classical risk model, the expected discounted penalty at ruin with a stochastic interest rate is considered. The interest rate randomness is described by standard Wiener process and Poisson process. Under this stochastic interest rate, the integro-differential equation and the renewal equation for the expected discounted penalty at ruin are derived respectively.