A Note on a Modified Parisian Ruin Concept

Eric C. K. Cheung () and Jeff T. Y. Wong
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Eric C. K. Cheung: School of Risk and Actuarial Studies, UNSW Business School, University of New South Wales, Sydney, NSW 2052, Australia
Jeff T. Y. Wong: Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong

Risks, 2023, vol. 11, issue 3, 1-15

Abstract: Traditionally, Parisian ruin is said to occur when the insurer’s surplus process has stayed below level zero continuously for a certain grace period. Inspired by this concept, in this paper we propose a modification by assuming that once a grace period has been granted when the surplus becomes negative, the surplus level will not be monitored continuously in the interim, but instead it will be checked at the end of the grace period to see whether the business has recovered. Under an Erlang distributed grace period, a computationally tractable formula for the Gerber–Shiu expected discounted penalty function is derived. Numerical examples regarding the modified Parisian ruin probability are also provided.

Keywords: compound poisson process; Parisian ruin; Erlangization; Gerber–Shiu function; discounted density (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2023
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