Discrete-time portfolio optimization under maximum drawdown constraint with partial information and deep learning resolution

TL;DR

This paper addresses discrete-time portfolio optimization with partial information and maximum drawdown constraints, employing Bayesian modeling, dynamic programming, and deep learning to derive solutions and analyze performance under drift uncertainty.

Contribution

It introduces a novel combination of Bayesian modeling, dynamic programming, and deep learning for portfolio optimization with drawdown constraints under partial information.

Findings

Deep learning effectively solves the stochastic control problem.

Learning strategies outperform non-learning ones under drift uncertainty.

The non-learning strategy converges to a no short-sale Merton problem as constraints vanish.

Abstract

We study a discrete-time portfolio selection problem with partial information and maxi\-mum drawdown constraint. Drift uncertainty in the multidimensional framework is modeled by a prior probability distribution. In this Bayesian framework, we derive the dynamic programming equation using an appropriate change of measure, and obtain semi-explicit results in the Gaussian case. The latter case, with a CRRA utility function is completely solved numerically using recent deep learning techniques for stochastic optimal control problems. We emphasize the informative value of the learning strategy versus the non-learning one by providing empirical performance and sensitivity analysis with respect to the uncertainty of the drift. Furthermore, we show numerical evidence of the close relationship between the non-learning strategy and a no short-sale constrained Merton problem, by illustrating the convergence of the former towards the latter as the maximum drawdown constraint vanishes.