带有确定投资回报的经典风险过程下的破产时罚金折现期望

The expected discounted penalty function at ruin during the classical risk process with deterministic return on investment

考虑带有确定投资回报的经典风险过程下,得到了破产时罚金折现期望的积分表达、连续可微性及其所满足的积分方程和积分微分方程,并且给出了关于积分方程的解的一些讨论.

The classical risk process with deterministic return on investment is considered . The Feller expression of the expected discounted penalty function at ruin is obtained, and its continuous differentiability is proved. Furthermore, the integral equation and integro-differential equation satisfied by the expected discounted penalty function at ruin are derived. Finally, some discussions about the solutions of integral equation are given.