Time-Inconsistent Markovian Control Problems Under Model Uncertainty With Application to the Mean-Variance Portfolio Selection

Abstract

In this paper, we study a class of time-inconsistent terminal Markovian control problems in discrete time subject to model uncertainty. We combine the concept of the sub-game perfect strategies with the adaptive robust stochastic control method to tackle the theoretical aspects of the considered stochastic control problem. Consequently, as an important application of the theoretical results and by applying a machine learning algorithm we solve numerically the mean-variance portfolio selection problem under the model uncertainty.

Nonparametric Adaptive Bayesian Stochastic Control Under Model Uncertainty

“…A related work is [4], which studies the topic by taking into account the transaction costs. The adaptive robust framework introduced in [7] incorporates reducing the uncertainty in the robust method, and is applied to time-inconsistent Markovian control problems under model uncertainty in the follow-up work [8].…”

Discrete‐time risk sensitive portfolio optimization with proportional transaction costs

“…Note that while mean‐variance trading might lead to time‐inconsistency, the risk‐sensitive trading is time‐consistent, see Bielecki and Pliska (2003); Bielecki et al. (2021) for details. Also, to better understand the difference between risk‐sensitive and risk‐neutral frameworks, we decided to include the results for strategy similar to (4) but with risk‐sensitivity parameter set to $$\gamma =-0.0005$$, which approximates the risk‐neutral setting, that is, strategy for γ close to zero, which is near Kelly (log‐growth) optimal, see Di Masi and Stettner (2006).…”

Discrete-time risk sensitive portfolio optimization with proportional transaction costs

“…For completeness, we also added values for entropy second-order Taylor expansion based on mean and variance which illustrates the link between risk-sensitive framework and mean-variance framework. Note that while mean-variance trading might lead to timeinconsistency, the risk-sensitive trading is time-consistent, see [7,4] for details. Also, to better understand the difference between risk-sensitive and risk-neutral frameworks, we decided to include the results for strategy similar to (4) but with risk-sensitivity parameter set to γ = −0.0005, which approximates the risk-neutral setting, see [21].…”