An operator-based approach to the analysis of ruin-related quantities in jump diffusion risk models

Runhuan Feng

Insurance: Mathematics and Economics, 2011, vol. 48, issue 2, 304-313

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.

Keywords: Jump; diffusion; process; Ruin; theory; Expected; discounted; penalty; at; ruin; Integro-differential; equation; Operator; calculus; Resolvent; density (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:48:y:2011:i:2:p:304-313

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