Precommitted Investment Strategy versus Time-Consistent Investment Strategy for a General Risk Model with Diffusion

Abstract

We mainly study a general risk model and investigate the precommitted strategy and the time-consistent strategy under mean-variance criterion, respectively. A lagrange method is proposed to derive the precommitted investment strategy. Meanwhile from the game theoretical perspective, we find the time-consistent investment strategy by solving the extended Hamilton-Jacobi-Bellman equations. By comparing the precommitted strategy with the time-consistent strategy, we find that the company under the time-consistent strategy has to give up the better current utility in order to keep a consistent satisfaction over the whole time horizon. Furthermore, we theoretically and numerically provide the effect of the parameters on these two optimal strategies and the corresponding value functions.