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
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
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
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
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
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