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 language | English (US) |
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Pages (from-to) | 304-313 |
Number of pages | 10 |
Journal | Insurance: Mathematics and Economics |
Volume | 48 |
Issue number | 2 |
DOIs | |
State | Published - Mar 2011 |
Externally published | Yes |
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