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Effect of Stop-Loss Reinsurance on Primary Insurer Solvency

Author

Listed:
  • 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)

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.

Suggested Citation

  • Corina Constantinescu & Alexandra Dias & Bo Li & David Šiška & Simon Wang, 2022. "Effect of Stop-Loss Reinsurance on Primary Insurer Solvency," Risks, MDPI, vol. 10(10), pages 1-15, October.
    • Handle: RePEc:gam:jrisks:v:10:y:2022:i:10:p:193-:d:937520
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    References listed on IDEAS

    as
    1. Borch, Karl, 1975. "Optimal Insurance Arrangements," ASTIN Bulletin, Cambridge University Press, vol. 8(3), pages 284-290, September.
    2. Albrecher, Hansjörg & Constantinescu, Corina & Pirsic, Gottlieb & Regensburger, Georg & Rosenkranz, Markus, 2010. "An algebraic operator approach to the analysis of Gerber-Shiu functions," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 42-51, February.
    3. Pervozvansky, A. Jr., 1998. "Equation for survival probability in a finite time interval in case of non-zero real interest force," Insurance: Mathematics and Economics, Elsevier, vol. 23(3), pages 287-295, December.
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