Absolute Ruin Probabilities in a Jump Diffusion Risk Model with Investment

Hans Gerber and Hailiang Yang

North American Actuarial Journal, 2007, vol. 11, issue 3, 159-169

Abstract: This article considers the compound Poisson insurance risk model perturbed by diffusion with investment. We assume that the insurance company can invest its surplus in both a risky asset and the risk-free asset according to a fixed proportion. If the surplus is negative, a constant debit interest rate is applied. The absolute ruin probability function satisfies a certain integro-differential equation. In various special cases, closed-form solutions are obtained, and numerical illustrations are provided.

Date: 2007
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DOI: 10.1080/10920277.2007.10597474

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