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

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)304-313
Number of pages10
JournalInsurance: Mathematics and Economics
Volume48
Issue number2
DOIs
StatePublished - Mar 2011
Externally publishedYes

Keywords

  • Expected discounted penalty at ruin
  • Integro-differential equation
  • Jump diffusion process
  • Operator calculus
  • Resolvent density
  • Ruin theory

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

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