Big Data Challenges of High‐Dimensional Continuous‐Time Mean‐Variance Portfolio Selection and a Remedy

Abstract

Investors interested in the global financial market must analyze financial securities internationally. Making an optimal global investment decision involves processing a huge amount of data for a high-dimensional portfolio. This article investigates the big data challenges of two mean-variance optimal portfolios: continuous-time precommitment and constant-rebalancing strategies. We show that both optimized portfolios implemented with the traditional sample estimates converge to the worst performing portfolio when the portfolio size becomes large. The crux of the problem is the estimation error accumulated from the huge dimension of stock data. We then propose a linear programming optimal (LPO) portfolio framework, which applies a constrained ℓ minimization to the theoretical optimal control to mitigate the risk associated with the dimensionality issue. The resulting portfolio becomes a sparse portfolio that selects stocks with a data-driven procedure and hence offers a stable mean-variance portfolio in practice. When the number of observations becomes large, the LPO portfolio converges to the oracle optimal portfolio, which is free of estimation error, even though the number of stocks grows faster than the number of observations. Our numerical and empirical studies demonstrate the superiority of the proposed approach.

Robust time-inconsistent stochastic control problems

“…Loosely speaking, from the perspective of decision making, precommitment policy emphasizes on global optimality while time-consistent policy emphasizes on local optimality. However, precommitment policy is sometimes inferior because its strong commitment leads to time-inconsistency in efficiency (see [Cui et al, 2010] for details and a remedy) and its error-accumulation property brings huge estimation error (see [Chiu et al, 2017]). Moreover, finding precommitment policy poses analytical challenges for general time-inconsistent stochastic control problems.…”

Simulation-based Value-at-Risk for nonlinear portfolios

“…We shall demonstrate our proposal via least absolute shrinkage and selection operator (LASSO; Tibshirani, 1996), or equivalently the constrained 1 minimization. Noteworthy, our proposal shares a similar view with Pun and Wong (2016), Chiu et al (2017) and Pun and Wong (2019) amongst others in the sense that the introduction of the LASSO penalty enables consistent estimation of the quantities of interest. For instance, Pun and Wong (2016) proved that the estimation errors of high-dimensional portfolio makes the optimal portfolio objective function diverge while our results demonstrate that, with appropriate shrinkage due to LASSO, the Longstaff and Schwartz's (2001) approach can be properly implemented under high-dimensional cases.…”

Big Data-Driven Cognitive Computing System for Optimization of Social Media Analytics

“…Similarly, some studies used uncertain approaches including stochastic programming [21] and robust optimization [22]. As one of the rare research works, Chiu et al [35] examined the big data challenges of high-dimensional continuous-time mean-variance portfolio selection problems. The aim was to estimate the total error accumulated from the huge dimension of stock data.…”