Absolute ruin probabilities in a jump diffusion risk model with investment. (English) Zbl 1480.91208
Summary: 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.
MSC:
| 91G05 | Actuarial mathematics |
| 60G55 | Point processes (e.g., Poisson, Cox, Hawkes processes) |
| 60J60 | Diffusion processes |
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