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Optimal risk transfers in insurance groups. (English) Zbl 1270.91028

Summary: 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.

MSC:

91B30 Risk theory, insurance (MSC2010)
90C90 Applications of mathematical programming
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