Optimal risk transfers in insurance groups
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Optimal risk transfers are derived within an insurance group consisting of two separate legal entities, operating under potentially different regulatory capital requirements and capital costs. Consistent with regulatory practice, capital requirements for each entity are computed by either a value-at-risk or an expected shortfall risk measure. The optimality criterion consists of minimising the risk-adjusted value of the total group liabilities, with valuation carried out using a cost-of-capital approach. The optimisation problems are analytically solved and it is seen that optimal risk transfers often involve the transfer of tail risk (unlimited reinsurance layers) to the more weakly regulated entity. We show that, in the absence of a capital requirement for the credit risk that specifically arises from the risk transfer, optimal risk transfers achieve capital efficiency at the cost of increasing policyholder deficit. However, when credit risk is properly reflected in the capital requirement, incentives for tail-risk transfers vanish and policyholder welfare is restored.
- Acerbi C, Tasche D (2002) On the coherence of expected shortfall. J Bank Finance 26(7):1487–1503 CrossRef
- Albrecher H, Thonhauser S (2009) Optimality results for dividend problems in insurance. RACSAM Rev R Acad Cien Ser A Mat 103(2):295–320 CrossRef
- Arrow KJ (1963) Uncertainty and the welfare economics of medical care. Am Econ Rev 53(5):941–973
- Artzner P, Delbaen F, Eber JM, Heath D (1999) Coherent measures of risk. Math Finance 9:203–228 CrossRef
- Bernard C, Tian W (2010) Insurance market effects of risk management metrics. Geneva Risk Insur Rev 35:47–80 CrossRef
- Borch K (1960) An attempt to determine the optimum amount of stop loss reinsurance. Trans 16th Int Cong Actuar I:597–610
- Cai J, Tan KS, Weng C, Zhang Y (2008) Optimal reinsurance under VaR and CTE risk measures. Insur Math Econ 43(1):185–196 CrossRef
- Carlier G, Dana R-A (2003) Pareto efficient insurance contracts when the insurer’s cost function is discontinuous. Econ Theory 21(4):871–893 CrossRef
- Centeno ML, Guerra M (2010) The optimal reinsurance strategy—the individual claim case. Insur Math Econ 46(3):450–460 CrossRef
- Cheung KC (2010) Optimal reinsurer revisited—a geometric approach. Astin Bull 40(1):221–239 CrossRef
- Chi Y, Tan KS (2011) Optimal reinsurance under VaR and CVaR risk measures: a simplified approach. Astin Bull 42(1):487–509
- Denuit M, Dhaene J, Goovaerts M, Kaas R (2005) Actuarial theory for dependent risks: measures, orders and models. Wiley, Chichester
- Dowd K, Blake D (2006) After VaR: the theory, estimation, and insurance applications of quantile-based risk measures. J Risk Insur 73(2):193–229 CrossRef
- Embrechts P, Hofert M (2010) A note on generalized inverses (Preprint).
- EIOPA: (2011). “Equivalence Assessment of the Swiss Supervisory System in Relation to Articles 172, 227 and 260 of the Solvency II Directive", EIOPA-BoS-11-028. https://eiopa.europa.eu/consultations/consultation-papers/index.html.
- EIOPA (2009) Advice for level 2 implementing measures on solvency II: supervision of risk concentration and intra-group transactions, CEIOPS-DOC-53/09. https://eiopa.europa.eu/consultations/consultation-papers/2010-2009-closed-consultations/index.html.
- European Commission (2009) Directive 2009/138/EC of the European Parliament and of the Council of 25 November 2009 on the taking-up and pursuit of the business of insurance and reinsurance (Solvency II). Off J Eur Union, L335.
- Federal Office of Private Insurance: 2006. The Swiss experience with market consistent technical provisions—the cost of capital approach. http://www.finma.ch/archiv/bpv/e/themen/00506/00552/00727/index.html.
- Filipović D, Kupper M (2008) Optimal capital and risk transfers for group diversification. Math Finance 18:55–76 CrossRef
- Gatzert N, Schmeiser H (2011) On the risk situation of financial conglomerates: does diversification matter? Financial Mark Portfolio Manag 25:3–26 CrossRef
- Guerra M, Centeno ML (2008) Optimal reinsurance policy: the adjustment coefficient and the expected utility criteria. Insur Math Econ 42(2):529–539 CrossRef
- Guerra M, Centeno ML (2010) Optimal reinsurance for variance related premium calculation principles. Astin Bull 40(1):97–121 CrossRef
- Van Heerwaarden AE, Kaas R, Goovaerts MJ (1989) Optimal reinsurer in the relation to ordering of risk. Insur Math Econ 8(1):11–17 CrossRef
- Hipp C, Vogt M (2003) Optimal dynamic XL reinsurance. Astin Bull 33(2):193–207 CrossRef
- Hürlimann V (2003) Conditional value-at-risk bounds for compound Poisson risks and a normal approximation. J Appl Math 3:141–153 CrossRef
- Kaluszka M (2001) Optimal reinsurance under mean-variance premium principles. Insur Math Econ 28(1):61–67 CrossRef
- Kaluszka M (2005) Truncated stop loss as optimal reinsurance agreement in one-period models. Astin Bull 35(2):337–349 CrossRef
- Kaluszka M, Okolewski A (2008) An extension of Arrow’s result on optimal reinsurance contract. J Risk Insur 75(2):275–288 CrossRef
- Keller P (2007) Group diversification. Geneva Pap 38:382–392 CrossRef
- Landsberger M, Meilijson II (1994) Comonotone allocations, Bickel Lehmann dispersion and the Arrow–Pratt measure of risk aversion. Ann Oper Res 52:97–106 CrossRef
- Ludkovski M, Young VR (2009) Optimal risk sharing under distorted probabilities. Math Financial Econ 2(2):87–105 CrossRef
- Myers SC, Read JA Jr (2001) Capital allocation for insurance companies. J Risk Insur 68(4):545–580 CrossRef
- Phillips RD, Cummins JD, Allen F (1998) Financial pricing of insurance in the multiple-line insurance company. J Risk Insur 65(4):597–636 CrossRef
- Schmidli H (2001) Optimal proportional reinsurance policies in a dynamic setting. Scand Actuar J 1:55–68 CrossRef
- Schmidli H (2002) On minimizing the ruin probability by investment and reinsurance. Ann Probab 12(3):890–907 CrossRef
- Schlütter S, Gründl H (2011) Who benefits from buildiung insurance groups? A welfare analysis based on optimal group risk management. ICIR working paper series Nr. 8. Goethe Universität, Frankfurt am Main
- Verlaak R, Beirlant J (2003) Optimal reinsurance programs: an optimal combination of several reinsurance protections on a heterogeneous insurance Portfolio. Insur Math Econ 33(2):381–403 CrossRef
- Wüthrich MV, Bühlmann H, Furrer H (2010) Market-consistent actuarial valuation, 2nd edn. Springer, Berlin
- Young VR (1999) Optimal insurance under Wang’s premium principle. Insur Math Econ 25(2):109–122 CrossRef
- Optimal risk transfers in insurance groups
European Actuarial Journal
Volume 3, Issue 1 , pp 159-190
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- Cost of capital
- Expected shortfall
- Insurance groups
- Optimal reinsurance