一类无穷时区上的时间不一致最优控制问题的均衡控制

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

摘要:

本文研究一类无穷时区上的时间不一致最优控制问题, 其中的目标泛函含有贴现函数, 且贴现率 充分大.在此类问题中， 贴现率不保持恒定使得问题具有时间不一致性，从而局部最优不再等价于整体最优, 因此我们考虑均衡控制而非最优控制. 运用针状变分的方法, 本文推导了容许控制成为均衡控制的充要条件. 当贴现函数为指数型时, 此结果便退化为无穷时区上的 Pontryagin 最大值原理. 最后我们给出该结果在经济学中的一个应用.

关键词:时间不一致控制问题，均衡控制，无穷时区，贴现率

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.

Key words:Time-inconsistent optimal control, Equilibrium control, Infinite horizon, Discount rate