Differentiability of dividends function on jump-diffusion risk process with a barrier dividend strategy. (English) Zbl 1321.60167
Summary: We consider a dividends model with a stochastic jump perturbed by diffusion. First, we prove that the expected discounted dividends function is twice continuously differentiable under the condition that the claim distribution function has continuous density. Then we show that the expected discounted dividends function under a barrier strategy satisfies some integro-differential equation of defective renewal type, and the solution of which can be explicitly expressed as a convolution formula. Finally, we study the Laplace transform of ruin time on the modified surplus process.
MSC:
| 60J75 | Jump processes (MSC2010) |
| 60J60 | Diffusion processes |
| 91B30 | Risk theory, insurance (MSC2010) |
| 91G80 | Financial applications of other theories |
Keywords:
jump-diffusion risk process; expected discounted dividends; ruin time; integro-differential equation; Laplace transform; barrier strategyReferences:
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