Equilibrium control of a class of time-inconsistent optimal control problems with infinite horizon

Abstract:

We study time-inconsistent optimal control problems with infnite horizon and dominating discount. In this problem, the non-constant discount rate results in the time inconsistency, thus local optimization is not equal to overall optimization anymore. Hence we study the equilibrium control instead of the optimal control. By using the needle variation method, we deduce the sufcient and necessary conditions for the equilibrium control. When the discount function has exponential form, our results degenerates to the Pontryagin maximum principle with infnite horizon. Finally, we given an example in economy.