Underwriting in Property-Casualty Insurance Markets : Regulation, Risk and Volatility

We offer a novel explanation of underwriting volatility in property-liability insurance markets in terms of private uncertainty over public regulatory policy. Underwriting involving random losses to policyholders is one source of risk to the equity value of insurance firms. Solvency regulations, however, pose a second source of risk to equity value when the implementation of such regulations randomly affects the return to underwriting but exhibits imperfect correlation with market conditions over time. Using a differential game in a standard no-arbitrage environment to model interaction between these two sources of risk, we derive the valuation equation for property-liability underwriting inclusive of the respective best-reply underwriting strategy of a representative insurance firm and the implementation strategy of a representative regulator. Owing to the conflicting effects of these strategies on firm equity, regulations adopted to reduce the solvency risk of insurers can, paradoxically, increase underwriting volatility in an otherwise efficient insurance market. Under certain parametric conditions, we also show that, even in the presence of complete financial markets, a subgame perfect Nash equilibrium of this game can exhibit a limit cycle in the value of underwriting which mirrors empirical evidence on the presence of cycles in property-liability insurance markets