Optimal Risk Transfers in Insurance Groups

The final version of this article has appeared as: Asimit A. V., Badescu, A. M., Tsanakas, A. (2013), 'Optimal Risk Transfers in Insurance Groups', European Actuarial Journal, 3(1), p.159-190

29 Pages Posted: 19 Jan 2012 Last revised: 3 Jan 2014

See all articles by Alexandru Vali Asimit

Alexandru Vali Asimit

Cass Business School, City, University of London

Alex Badescu

University of Calgary

Andreas Tsanakas

City University London - Cass Business School

Date Written: January 18, 2012

Abstract

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. Consistently 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 minimizing the risk-adjusted value of the total group liabilities, with valuation carried out using a cost-of-capital approach. The optimization 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 arising 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.

Keywords: Cost of Capital, Expected Shortfall, Insurance Groups, Optimal Reinsurance, Value-at-Risk

Suggested Citation

Asimit, Alexandru Vali and Badescu, Alex and Tsanakas, Andreas, Optimal Risk Transfers in Insurance Groups (January 18, 2012). The final version of this article has appeared as: Asimit A. V., Badescu, A. M., Tsanakas, A. (2013), 'Optimal Risk Transfers in Insurance Groups', European Actuarial Journal, 3(1), p.159-190. Available at SSRN: https://ssrn.com/abstract=1987783 or http://dx.doi.org/10.2139/ssrn.1987783

Alexandru Vali Asimit (Contact Author)

Cass Business School, City, University of London ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

Alex Badescu

University of Calgary ( email )

University of Calgary
Calgary, Alberta
Canada

Andreas Tsanakas

City University London - Cass Business School ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

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