A proof of a conjecture in the Cram\'er-Lundberg model with investments

Shimao Fan, Sheng Xiong and Wei-Shih Yang

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Abstract: In this paper, we discuss the Cram\'er-Lundberg model with investments, where the price of the invested risk asset follows a geometric Brownian motion with drift $a$ and volatility $\sigma> 0.$ By assuming there is a cap on the claim sizes, we prove that the probability of ruin has at least an algebraic decay rate if $2a/\sigma^2 > 1$. More importantly, without this assumption, we show that the probability of ruin is certain for all initial capital $u$, if $2a/\sigma^2 \le 1$.

Date: 2010-02
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1003.0135

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