An operator-based approach to the analysis of ruin-related quantities in jump diffusion risk models
AbstractRecent 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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Bibliographic InfoArticle provided by Elsevier in its journal Insurance: Mathematics and Economics.
Volume (Year): 48 (2011)
Issue (Month): 2 (March)
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Web page: http://www.elsevier.com/locate/inca/505554
Jump diffusion process Ruin theory Expected discounted penalty at ruin Integro-differential equation Operator calculus Resolvent density;
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