A non-zero-sum reinsurance-investment game with delay and asymmetric information

In this paper, we investigate a non-zero-sum stochastic differential reinsurance-investment game problem between two insurers. Both insurers can purchase proportional reinsurance and invest in financial market that contains risk-free asset risky asset. We consider the insurers' wealth processes with delay to characterize bounded memory feature. For considering effect of asymmetric information, assume have access different levels information market. Each insurer's objective is maximize expected utility its performance relative competitor. derive Hamilton-Jacobi-Bellman (HJB) equations general Nash equilibrium strategies associated control by applying dynamic programming principle. constant absolute risk aversion (CARA) insurers, explicit value functions are obtained. Finally, present some numerical studies draw economic interpretations find following interesting results: (1) insurer less completely ignores own factor, but imitates investment strategy competitor who has more on market, which manifestation herd economics; (2) difference effects weights related length time framework game, illustrates should rationally estimate correlation historical future based their tolerance, especially when decision makers over long period time.