Equilibrium reinsurance and investment strategies under preference ambiguity

This paper studies an insurer's reinsurance and investment problem when the risk aversion coefficient is random, and the insurer exhibits preference ambiguity toward this uncertainty. The insurer can purchase pre-loss reinsurance and allocate wealth between a risky asset and a risk-free asset. Preferences are modeled by the mean–variance criterion under ambiguity with random risk aversion, i.e. preference ambiguity, yielding a time-inconsistent control problem. Using an equilibrium approach, we establish a verification theorem and an extended HJB system that delivers closed-form equilibrium strategies. A key insight is that the preference ambiguity framework endogenously links reinsurance and investment decisions, even when insurance and financial risks are statistically independent. This breaks the separability implied by classical CARA, mean–variance, or robust preferences under model uncertainty. The framework thus rationalizes empirically observed ‘risk-alignment effect’ whereby insurers reduce investment risk following underwriting losses or heightened underwriting volatility. Ambiguity further induces a time-decaying distortion that vanishes at maturity, with all strategies converging to their ambiguity-neutral benchmarks. Comparative statics show that the strength of these effects is governed by the dispersion of the risk aversion distribution.