Finite-time ruin probabilities under large-claim reinsurance treaties for heavy-tailed claim sizes
Journal of Applied Probability , Volume 57 - Issue 2 p. 513- 530
We investigate the probability that an insurance portfolio gets ruined within a finite time period under the assumption that the r largest claims are (partly) reinsured. We show that for regularly varying claim sizes the probability of ruin after reinsurance is also regularly varying in terms of the initial capital, and derive an explicit asymptotic expression for the latter. We establish this result by leveraging recent developments on sample-path large deviations for heavy tails. Our results allow, on the asymptotic level, for an explicit comparison between two well-known large-claim reinsurance contracts, namely LCR and ECOMOR. Finally, we assess the accuracy of the resulting approximations using state-of-the-art rare event simulation techniques.
|, , , ,|
|Journal of Applied Probability|
|Rare events: Asymptotics, Algorithms, Applications|
|Organisation||Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands|
Albrecher, H, Chen, B, Vatamidou, E, & Zwart, A.P. (2020). Finite-time ruin probabilities under large-claim reinsurance treaties for heavy-tailed claim sizes. Journal of Applied Probability, 57(2), 513–530. doi:10.1017/jpr.2020.8