Solvency II, regulatory capital, and optimal reinsurance: How good are Conditional Value-at-Risk and spectral risk measures?

Mario Brandtner and Wolfgang Kürsten

Insurance: Mathematics and Economics, 2014, vol. 59, issue C, 156-167

Abstract: We study the problem of optimal reinsurance as a means of risk management in the regulatory framework of Solvency II under Conditional Value-at-Risk and, as its natural extension, spectral risk measures. First, we show that stop-loss reinsurance is optimal under both Conditional Value-at-Risk and spectral risk measures. Spectral risk measures thus constitute a more general class of suitable regulatory risk measures than specific Conditional Value-at-Risk. At the same time, the established type of stop-loss reinsurance can be maintained as the optimal risk management strategy that minimizes regulatory capital. Second, we derive the optimal deductibles for stop-loss reinsurance. We show that under Conditional Value-at-Risk, the optimal deductible tends towards restrictive and counter-intuitive corner solutions or “plunging”, which is a serious objection against its use in regulatory risk management. By means of the broader class of spectral risk measures, we are able to overcome this shortcoming as optimal deductibles are now interior solutions. Especially, the recently discussed power spectral risk measures and the Wang risk measure are shown to avoid any plunging. They yield a one-to-one correspondence between the risk parameter and the optimal deductible and, thus, provide economically plausible risk management strategies.

Keywords: Optimal reinsurance; Stop-loss; Optimal deductible; Spectral risk measures; Conditional Value-at-Risk (search for similar items in EconPapers)
JEL-codes: C44 D81 G22 (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:59:y:2014:i:c:p:156-167

DOI: 10.1016/j.insmatheco.2014.09.008

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