Analysis of the expected discounted penalty function for a general jump-diffusion risk model and applications in finance

Yichun Chi

Insurance: Mathematics and Economics, 2010, vol. 46, issue 2, 385-396

Abstract: In this paper, we extend the Cramér-Lundberg risk model perturbed by diffusion to incorporate the jumps of surplus investment return. Under the assumption that the jump of surplus investment return follows a compound Poisson process with Laplace distributed jump sizes, we obtain the explicit closed-form expression of the resulting Gerber-Shiu expected discounted penalty (EDP) function through the Wiener-Hopf factorization technique instead of the integro-differential equation approach. Especially, when the claim distribution is of Phase-type, the expression of the EDP function is simplified even further as a compact matrix-type form. Finally, the financial applications include pricing barrier option and perpetual American put option and determining the optimal capital structure of a firm with endogenous default.

Keywords: Gerber-Shiu; expected; discounted; penalty; function; Wiener-Hopf; factorization; Perturbed; compound; Poisson; risk; process; Laplace; distribution; Perpetual; American; put; option; Barrier; option; Optimal; capital; structure (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:46:y:2010:i:2:p:385-396

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