An operator-based approach to the analysis of ruin-related quantities in jump diffusion risk models |
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Authors: | Runhuan Feng |
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Institution: | Department of Mathematical Sciences, University of Wisconsin - Milwaukee, P.O. Box 413, Milwaukee, WI, 53202-0413, USA |
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Abstract: | Recent developments in ruin theory have seen the growing popularity of jump diffusion processes in modeling an insurer’s assets and liabilities. Despite the variations of technique, the analysis of ruin-related quantities mostly relies on solutions to certain differential equations. In this paper, we propose in the context of Lévy-type jump diffusion risk models a solution method to a general class of ruin-related quantities. Then we present a novel operator-based approach to solving a particular type of integro-differential equations. Explicit expressions for resolvent densities for jump diffusion processes killed on exit below zero are obtained as by-products of this work. |
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Keywords: | Jump diffusion process Ruin theory Expected discounted penalty at ruin Integro-differential equation Operator calculus Resolvent density |
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