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Title: Robust on-line portfolio selection via adaptive conditional volatility estimation Authors:  Minyoung Kim - Seoul National University of Science and Technology (Korea, South) [presenting]
Abstract: In the on-line portfolio selection problem, the principle of the moving average reversion (MAR) has received significant attention recently. However, most MAR-based approaches focused on the point estimates of the MAR, unable to deal with its volatility, leading to non-robust strategies. We propose a quite simple but reasonable volatility model: a conditional volatility model where the volatility of the return is assumed to be a function of the MAR estimate. It is motivated from the observation that the volatility tends to be high when the MAR estimate is positively large, and vice versa, which is indeed verified in several market historic data. We specifically model this phenomenon as a simple step function comprised of two sets of parameters, the MAR threshold and the levels of the volatility. These parameters are adaptively estimated from the latest data via Bayesian inference where we place conjugate priors (e.g., scaled-inverse-chi2) on them. With this volatility model, we optimize the portfolio using the worst-case Value-At-Risk method, which can be formulated as an SDP optimization that admits many efficient solvers. Additionally, the method becomes more robust since it makes no assumption on specific distributions (e.g., Gaussians) beyond the second-order moment constraints. We empirically demonstrate the benefits of the proposed approach on various real stock market data.