Alpha-robust mean–variance reinsurance and investment strategies with transaction costs

This paper investigates the time-consistent reinsurance and investment strategies for insurers based on the alpha-robust mean–variance criterion. We assume that transaction costs with quadratic form exist in the financial market composed of a risk-free asset and $n$ risky assets, and the insurance and financial markets are correlated. By solving a system of extended HJB equations, the equilibrium reinsurance and investment strategy and the corresponding value function are derived in terms of the solution to a system of matrix Riccati equations. In some special cases, more explicit expressions for the equilibrium strategies and value functions are provided. Numerical examples demonstrate that the growth rate of investment slows down as the transaction costs level or the correlation coefficient increases. In addition, we find that the transaction costs level has opposite effects on the utility losses due to ignoring jumps or ambiguity.