Effect of Stop-Loss Reinsurance on Primary Insurer Solvency

Constantinescu, Corina ORCID: 0000-0002-5219-3022, Dias, Alexandra, Li, Bo, Šiška, David and Wang, Simon (2022) Effect of Stop-Loss Reinsurance on Primary Insurer Solvency Risks, 10 (10). p. 193. ISSN 2227-9091, 2227-9091

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Abstract

Stop-loss reinsurance is a risk management tool that allows an insurance company to transfer part of their risk to a reinsurance company. Ruin probabilities allow us to measure the effect of stop-loss reinsurance on the solvency of the primary insurer. They further permit the calculation of the economic capital, or the required initial capital to hold, corresponding to the 99.5% value-at-risk of its surplus. Specifically, we show that under a stop-loss contract, the ruin probability for the primary insurer, for both a finite- and infinite-time horizon, can be obtained from the finite-time ruin probability when no reinsurance is bought. We develop a finite-difference method for solving the (partial integro-differential) equation satisfied by the finite-time ruin probability with no reinsurance, leading to numerical approximations of the ruin probabilities under a stop-loss reinsurance contract. Using the method developed here, we discuss the interplay between ruin probability, reinsurance retention level and initial capital.

Item Type:	Article
Uncontrolled Keywords:	finite-difference method, reinsurance, ruin probability, stop-loss
Depositing User:	Symplectic Admin
Date Deposited:	12 Oct 2022 08:15
Last Modified:	16 Jun 2026 08:56
DOI:	10.3390/risks10100193
Open Access URL:	https://doi.org/10.3390/risks10100193
Related Websites:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3165404
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