Effect of stop-loss reinsurance on the primary insurer solvency

Corina Constantinescu, Alexandra Dias*, Bo Li, David Siska, Simon Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Article number193
Number of pages15
Issue number10
Publication statusPublished - 10 Oct 2022


  • Finite-difference method
  • Reinsurance
  • Ruin probability
  • Stop-loss

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