Absolute ruin probabilities in a jump diffusion risk model with investment

Hans Gerber; Hailiang Yang

doi:10.1080/10920277.2007.10597474

Absolute ruin probabilities in a jump diffusion risk model with investment

Hans Gerber
, Hailiang Yang^*

^*Corresponding author for this work

University of Lausanne
The University of Hong Kong

Research output: Contribution to journal › Article › peer-review

55 Citations (Scopus)

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.

Original language	English
Pages (from-to)	159-169
Journal	North American Actuarial Journal
Volume	11
Issue number	3
DOIs	https://doi.org/10.1080/10920277.2007.10597474
Publication status	Published - Jul 2007
Externally published	Yes

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10.1080/10920277.2007.10597474

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title = "Absolute ruin probabilities in a jump diffusion risk model with investment",

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.",

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AB - 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.

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Absolute ruin probabilities in a jump diffusion risk model with investment

Abstract

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