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arXiv · 2104.14334

A constructive approach to existence of equilibria in time-inconsistent stochastic control problems

Jiang Yu Nguwi·Nicolas Privault
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Abstract

We extend the construction of equilibria for linear-quadratic and mean-variance portfolio problems available in the literature to a large class of mean-field time-inconsistent stochastic control problems in continuous time. Our approach relies on a time discretization of the control problem via n-person games, which are characterized via the maximum principle using Backward Stochastic Differential Equations (BSDEs). The existence of equilibria is proved by applying weak convergence arguments to the solutions of n-person games. A numerical implementation is provided by approximating n-person games using finite Markov chains.

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Jiang Yu Nguwi, Nicolas Privault. 2021-04-29. A constructive approach to existence of equilibria in time-inconsistent stochastic control problems. https://arxiv.org/abs/2104.14334

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