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Mitchell A. Polinsky & Steven Shavell, Subrogation and the Theory of Insurance When Suits Can Be Brought for Losses Suffered, 34 J.L. Econ. & Org. 619 (2018).

Abstract: The theory of insurance is considered here when an insured individual may be able to sue another party for the losses that the insured suffered—and thus when an insured has a potential source of compensation in addition to insurance coverage. Insurance policies reflect this possibility through so-called subrogation provisions that give insurers the right to step into the shoes of insureds and to bring suits against injurers. In a basic case, the optimal subrogation provisions involve full retention by the insurer of the proceeds from a successful suit and the pursuit of all positive expected value suits. This eliminates litigation risks for insureds and results in lower premiums—financed by the litigation income of insurers, including from suits that insureds would not otherwise have brought. Moreover, optimal subrogation provisions are characterized in the presence of moral hazard, administrative costs, and non-monetary losses, and it is demonstrated that optimal provisions entail sharing litigation proceeds with insureds in the first two cases but not when losses are non-monetary.