Optimal risk transfers in insurance groups
Insurance groups often comprise a number of distinct legal entities, operating in different territories. Diversification across an insurance group is no trivial matter and the way it operates depends on the group's legal structure.
On the one hand, the risk exposures of different entities will in general not be perfectly correlated, and thus some group level diversification is observed (e.g. by a parent company).
On the other hand, risks and assets in the group portfolio are not pooled across entities; hence there are limits to the cross-subsidy, as well as the capital fungibility, within the group.
Nonetheless, the risk and capital requirements of individual entities can be reduced, through a web of capital and risk transfer arrangements across entities.
The complexity of group legal structures and intra-group risk transfers, with entities being potentially subject to different regulatory regimes, poses a major challenge for regulators.
In comparison to previous literature on this topic, the focus here is on deriving optimal functional forms of risk transfers. 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 minimising the risk-adjusted value of the total group liabilities, with valuation carried out using a cost-of-capital approach.
It is found that optimal risk transfers often involve the transfer of tail risk (unlimited reinsurance layers) to the more weakly regulated entity. In addition, 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.
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