关键词: Gerber-Shiu折现罚金函数, 破产前瞬间盈余, 赤字, 折现因子

Abstract:

The  paper  studies the ruin problems for a renewal risk model with interest. An integral equation for the Gerber-Shiu discounted penalty function and an explicit infinite series expression for the Gerber-Shiu discounted penalty function are obtained. Then the authors generalize the Gerber-Shiu's formula$^{[4]}$   to this renewal risk process including the force of interest. Finally, as an application of the above results, an
exponential upper bound for the ultimate probability is derived by recursive technique.

Key words: Gerber-Shiu discounted penalty function, Surplus immediately prior to ruin, Deficit at ruin, Discounting factor