Optimal robust reinsurance-investment strategies for insurers with mean reversion and mispricing

Abstract

This paper considers how to optimize reinsurance and investment decisions for an insurer who has aversion to model ambiguity, who wants to take into consideration time-varying investment conditions via mean reverting models, and who wants to take advantage of statistical arbitrage opportunities afforded by mispricing of stocks. We work under a complex realistic environment: The surplus process is described by a jump–diffusion model and the financial market contains a market index, a risk-free asset, and a pair of mispriced stocks, where the expected return rate of the stocks and the mispricing follow mean reverting stochastic processes which take into account liquidity constraints. The insurer is allowed to purchase reinsurance and to invest in the financial market. We formulate an optimal robust reinsurance-investment problem under the assumption that the insurer is ambiguity-averse to the uncertainty from the financial market and to the uncertainty of the insured’s claims. Ambiguity aversion is an aversion to the uncertainty taken by making investment decisions based on a misspecified model. By employing the dynamic programming approach, we derive explicit formulae for the optimal robust reinsurance-investment strategy and the optimal value function. Numerical examples are presented to illustrate the impact of some parameters on the optimal strategy and on utility loss functions. Among our various practical findings and recommendations, we find that strengthened market liquidity significantly increases the demand for hedging from the mispriced market, to take advantage of the statistical arbitrage it affords.