Ruin Probabilities with Dependence on the Number of Claims within a Fixed Time Window



Constantinescu, Corina ORCID: 0000-0002-5219-3022, Dai, Suhang, Ni, Weihong and Palmowski, Zbigniew
(2016) Ruin Probabilities with Dependence on the Number of Claims within a Fixed Time Window. RISKS, 4 (2). p. 17.

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Abstract

We analyse the ruin probabilities for a renewal insurance risk process with inter-arrival time distributions depending on the claims that arrived within a fixed (past) time window. This dependence could be explained through a regenerative structure. The main inspiration of the model comes from the Bonus-Malus feature. We discuss first asymptotic results of ruin probabilities for different regimes of claim distributions. For numerical results, we recognise an embedded Markov additive process. Via an appropriate change of measure, ruin probabilities could be computed to a closed form formulae. Additionally, we present simulated results via the importance sampling method, which further permit an in-depth analysis of a few concrete cases.

Item Type: Article
Additional Information: ## TULIP Type: Articles/Papers (Journal) ##
Uncontrolled Keywords: regenerative risk process, ruin probability, subexponential distribution, Cramer asymptotics, importance sampling, crude Monte Carlo, Markov additive process
Depositing User: Symplectic Admin
Date Deposited: 16 Jun 2016 14:24
Last Modified: 19 Jan 2023 07:35
DOI: 10.3390/risks4020017
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3001697