Effect of Stop-Loss Reinsurance on Primary Insurer Solvency

Corina Constantinescu, Alexandra Dias (), Bo Li, David Šiška and Simon Wang
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Corina Constantinescu: Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, UK
Alexandra Dias: School for Business and Society, University of York, York YO10 5ZF, UK
Bo Li: Department of Mathematical Finance and Actuarial Science, Nankai University, Tianjin 300071, China
David Šiška: School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, UK
Simon Wang: Stable, London EH8 9AB, UK

Risks, 2022, vol. 10, issue 10, 1-15

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.

Keywords: finite-difference method; reinsurance; ruin probability; stop-loss (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2022
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