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.
Lidong Zhang. Ximin Rong. Ziping Du. "Precommitted Investment Strategy versus Time-Consistent Investment Strategy for a General Risk Model with Diffusion." Abstr. Appl. Anal. 2014 (SI19) 1 - 15, 2014. https://doi.org/10.1155/2014/358623