Ruin probability in the Cramer-Lundberg model with risky investments

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:121

Article

Xiong, Sheng¹  Yang, Wei-Shih¹ 

[1] Temple Univ, Dept Math, Philadelphia, PA 19122 USA

关键词: Cramer-Lundberg model;    Geometric Brownian motion;    Ruin probability;   

DOI  :  10.1016/j.spa.2011.01.008

来源: Elsevier

【 摘 要 】

We consider the Cramer-Lundberg model with investments in an asset with large volatility, where the premium rate is a bounded nonnegative random function c(t) and the price of the invested risk asset follows a geometric Brownian motion with drift a and volatility sigma > 0. It is proved by Pergamenshchikov and Zeitouny that the probability of ruin, psi(u), is equal to 1, for any initial endowment u >= 0, if rho := 2a/sigma(2) <= 1 and the distribution of claim size has an unbounded support. In this paper, we prove that psi(u) = 1 if rho <= 1 without any assumption on the positive claim size. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

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