Optimal Reinsurance in the Presence of Counterparty Default Risk

17 Pages Posted: 7 May 2013 Last revised: 17 Nov 2014

See all articles by Alexandru Vali Asimit

Alexandru Vali Asimit

City University London - The Business School

Alexandru Badescu

University of Calgary

Ka Chun Cheung

The University of Hong Kong

Date Written: May 7, 2013

Abstract

The optimal reinsurance arrangement is identified whenever the reinsurer counterparty default risk is incorporated in a one-period model. Our default risk model allows the possibility for the reinsurer to fail paying in full the promised indemnity, whenever it exceeds the level of regulatory capital. We also investigate the change in the optimal solution if the reinsurance premium recognises or not the default in payment. Closed form solutions are elaborated when the insurer's objective function is set via some well-known risk measures. It is also discussed the effect of reinsurance over the policyholder welfare. If the insurer is Value-at-Risk regulated, then the reinsurance does not increase the policyholder's exposure for any possible reinsurance transfer, even if the reinsurer may default in paying the promised indemnity. Numerical examples are also provided in order to illustrate and conclude our findings. It is found that the optimal reinsurance contract does not usually change if the counterparty default risk is taken into account, but one should consider this effect in order to properly measure the policyholders's exposure. In addition, the counterparty default risk may change the insurer's ideal arrangement if the buyer and seller have very different views on the reinsurer's recovery rate.

Keywords: Counterparty Default Risk, Distorted Risk Measure, Expected Policyholder Deficit, Premium Principle, Optimal Reinsurance, Value-at-Risk

JEL Classification: G22, D81

Suggested Citation

Asimit, Alexandru Vali and Badescu, Alexandru and Cheung, Ka Chun, Optimal Reinsurance in the Presence of Counterparty Default Risk (May 7, 2013). Insurance: Mathematics and Economics, 2013, Volume 53, issue 3, p. 690–697, Available at SSRN: https://ssrn.com/abstract=2261603 or http://dx.doi.org/10.2139/ssrn.2261603

Alexandru Vali Asimit (Contact Author)

City University London - The Business School ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

Alexandru Badescu

University of Calgary ( email )

University of Calgary
Calgary, Alberta
Canada

Ka Chun Cheung

The University of Hong Kong ( email )

Pokfulam Road
Hong Kong, Pokfulam HK
China

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