关键词: 风险理论, 预警区, 复合Poisson风险模型, 常利率

Abstract:

In this paper, the authors discuss the duration of negative surplus of the classical compound Poisson risk model with constant interest force. By presenting a new approach different from the martingale method proposed by Gerber (1990), the moment generating functions and the moments of both the single and total duration of negative surplus are formulated. Explicit expressions are given when the claim is exponentially distributed. Finally, the influence of interest force on the duration of negative surplus is illustrated by numerical results.

Key words: Risk theory, Duration of negative surplus, Compound Poisson risk model, Constant interest force