A dynamic approach for some time inconsistent problems

Jianfeng Zhang
University of Southern California (USC)

There are typically two strategies for time inconsistent problems: strategy of precommitment and strategy of consistent planning, which induce different value functions. The latter is a game approach where the player plays with infinitely many future selves, and most papers in continuous time models follow this approach. However, in situation where frequent "reneogotiation" is not allowed, the strategy of precommitment is more appropriate and it is the subject of this work. We first note that, many time inconsistent problems in the literature can be transformed into an optimization of a multiple (possibly infinite) dimensional controlled Backward SDE. We shall introduce a type of "forward utility" so that the problem, which is time inconsistent under the original fixed utility, becomes time consistent under our forward utility. We next characterize our forward utility as a solution to certain McKean-Vlasov type of equations. The talk will be based on some preliminary joint work with Jin Ma and Chandu Karnam.

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