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Discounted probability of exponential parisian ruin: Diffusion approximation

Part of: Miscellaneous special kernels Integro-ordinary differential equations Integral, integro-differential, and pseudodifferential operators

Published online by Cambridge University Press:  18 February 2022

Xiaoqing Liang Open the ORCID record for Xiaoqing Liang [Opens in a new window]  and
Virginia R. Young
Xiaoqing Liang*
Affiliation:
Hebei University of Technology
Virginia R. Young*
Affiliation:
University of Michigan
*
*Postal address: Department of Statistics, School of Sciences, Hebei University of Technology, Tianjin 300401, P. R. China. Email address: liangxiaoqing115@hotmail.com
**Postal address: Department of Mathematics, University of Michigan, Ann Arbor, Michigan, 48109. Email address: vryoung@umich.edu
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Abstract

We analyze the discounted probability of exponential Parisian ruin for the so-called scaled classical Cramér–Lundberg risk model. As in Cohen and Young (2020), we use the comparison method from differential equations to prove that the discounted probability of exponential Parisian ruin for the scaled classical risk model converges to the corresponding discounted probability for its diffusion approximation, and we derive the rate of convergence.

Keywords

Exponential Parisian ruinCramér–Lundberg risk modeldiffusion approximationasymptotic analysis

MSC classification

Primary: 90C59: Approximation methods and heuristics
Secondary: 47G20: Integro-differential operators 45J05: Integro-ordinary differential equations
Type
Original Article
Information
Journal of Applied Probability , Volume 59 , Issue 1 , March 2022 , pp. 17 - 37
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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