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We analyze multiline pricing and capital allocation in equilibriumno-arbitrage markets. Existing theories often assume a perfect complete market,but when pricing is linear, there is no diversification benefit from riskpooling and therefore no role for insurance companies. Instead of a perfectmarket, we assume a non-additive distortion pricing functional and theprinciple of equal priority of payments in default. Under these assumptions, wederive a canonical allocation of premium and margin, with properties that meritthe name the natural allocation. The natural allocation gives non-negativemargins to all independent lines for default-free insurance but can exhibitnegative margins for low-risk lines under limited liability. We introduce novelconditional expectation measures of relative risk within a portfolio and usethem to derive simple, intuitively appealing expressions for risk margins andcapital allocations. We give a unique capital allocation consistent with ourlaw invariant pricing functional. Such allocations produce returns that vary byline, in contrast to many other approaches. Our model provides a bridge betweenthe theoretical perspective that there should be no compensation for bearingdiversifiable risk and the empirical observation that more risky lines fetchhigher margins relative to subjective expected values.

Pricing and Capital Allocation for Multiline Insurance Firms With Finite Assets in an Imperfect Market