Neural Stochastic Control Application : Optimal Portfolio Allocation

Abstract

Neural Control (NC) is a growing field in stochastic optimal control applied to various dynamical systems such as quadcopter. NC is a non-parametric, learning based computational scheme, capable of handling high dimensional control problems. In this paper, “NC” principles have been applied to the problem of optimal investment portfolio allocation, which is commonly solved by the usage of covariance matrix in a Markowitz framework. Therefore, the portfolio quadratic optimization problem has been first re-cast into a generic stochastic control framework with non-linear dependencies and then solved using various Neural Networks (NNs). In NC context, literature on stacked Feed-Forward for time independent control has been recalled to formulate the properties of new NN architectures: Long Short-Term Memory (LSTM) and Attention LSTM for time-dependent control. Final section presents the numerical results of control weights convergence and dynamics using Monte Carlo simulation of portfolio asset prices (Geometric Brownian Motion) through various scenarios: first using stationary regime of volatility and correlation, second using non-stationary regime. Thus, behaviour of three NN architectures has been studied in those scenarios. Results suggest the further development of NC in domain of portfolio allocation as alternative of covariance matrix based solutions and related finance, economic supply and demand problems.