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Analysis of the expected discounted penalty function for a general jump-diffusion risk model and applications in finance. (English) Zbl 1231.91162
Summary: 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.

MSC:
91B30 Risk theory, insurance (MSC2010)
91G20 Derivative securities (option pricing, hedging, etc.)
60J75 Jump processes (MSC2010)
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