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This article studies the optimal mean-variance reinsurance-investment selection for insurers with mispricing. Assuming that insurers wish to purchase proportional/excess-of-loss reinsurance and exchange among a risk-free asset, a pair of mispriced stocks, and the market index to maximize their return and minimize the risk. Using the approach developed by Björk, Khapko, and Murgoci (Finance and Stochastics  2017 ; 21 (2):331–60), we derive the equilibrium strategies and the corresponding equilibrium value functions under two cases through solving the extended Hamilton–Jacobi–Bellman system. Moreover, numerical analyses are provided to illustrate our results.

Optimal reinsurance–investment policies for insurers with mispricing under mean-variance criterion