Analysis of the expected discounted penalty function for a general jump-diffusion risk model and applications in finance
AbstractIn 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Insurance: Mathematics and Economics.
Volume (Year): 46 (2010)
Issue (Month): 2 (April)
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Web page: http://www.elsevier.com/locate/inca/505554
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;
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