Time-consistent equilibrium reinsurance-investment strategy for n competitive insurers under a new interaction mechanism and a general investment framework

We propose a new interaction mechanism for n >= 2 competitive insurers, under which we investigate the time-consistent equilibrium reinsurance-investment strategy for n insurers. Each insurer can purchase reinsurance for reducing the claim risk and invest in the financial market for increasing his wealth. We consider a general investment framework which includes typical diversified and concentrated investment patterns in the literature. The objective of each insurer is to find a time-consistent equilibrium reinsurance-investment strategy so as to maximize the expected terminal wealth while minimizing the variance of the terminal wealth. By using the stochastic control technique, we obtain the explicit time-consistent equilibrium reinsurance-investment strategies and corresponding equilibrium value functions. Through analyzing the general investment strategy, we find the criterion of whether the insurer should invest in a specific risky asset. Furthermore, we examine theoretically and numerically how the price parameters of risky assets affect the concrete investment pattern. We find that when the appreciation rate of one risky asset exceeds some times as those of other risky assets, the insurer will only invest in this asset; otherwise, the insurer will adopt the diversified investment pattern. We also numerically examine the influences of the number of insurers and the surplus jump on the time-consistent equilibrium reinsurance strategy. (C) 2020 The Author(s). Published by Elsevier B.V.