Approximate Dynamic Programming-Based Dynamic Portfolio Optimization for Constrained Index Tracking

Abstract

Recently, the constrained index tracking problem, in which the task of trading a set of stocks is performed so as to closely follow an index value under some constraints, has often been considered as an important application domain for control theory. Because this problem can be conveniently viewed and formulated as an optimal decision-making problem in a highly uncertain and stochastic environment, approaches based on stochastic optimal control methods are particularly pertinent. Since stochastic optimal control problems cannot be solved exactly except in very simple cases, approximations are required in most practical problems to obtain good suboptimal policies. In this paper, we present a procedure for finding a suboptimal solution to the constrained index tracking problem based on approximate dynamic programming. Illustrative simulation results show that this procedure works well when applied to a set of real financial market data.

Some Observations for Portfolio Management Applications of Modern Machine Learning Methods

“…We apply a simplified version of the sparse Gaussian process (GP) classification method, which is a direct result of two recent remarkable Gaussian process papers [25,26], for performing risk sensitivity classification in dealing with financial portfolio management. Since portfolio management problems are optimal decision-making problems that rely on actual empirical data, theoretical and practical solutions can be formulated via many of recent machine learning and control advancements: the traditional mean-variance efficient portfolio problem [11]; index tracking portfolio formulation [12][13][14][15]; risk-adjusted expected return maximizing strategy [16][17][18]; trend following strategy [19][20][21][22][23]; long-short trading strategy (including the pairs trading strategy) [20,24], etc. In this paper, we also raise two important portfolio management issues in which the GP application results can be useful.…”

Modern Probabilistic Machine Learning and Control Methods for Portfolio Optimization

“…In particular, since portfolio optimization problems are essentially optimal decision-making problems that rely on actual data observed in a stochastic environment, theoretical and practical solutions can be formulated in light of recent advancements. These problems include the traditional mean-variance efficient portfolio problem [10], index tracking portfolio formulation [6][7][8]11], risk-adjusted expected return maximizing strategy [1,2,12], trend following strategy [13][14][15][16][17], long-short trading strategy (including the pairs trading strategy) [13,[18][19][20], and behavioral portfolio management.…”