Robust Portfolio Control with Stochastic Factor Dynamics

Glasserman, Paul; Xu, Xingbo

doi:10.2139/ssrn.1960723

Cited by 21 publications

(14 citation statements)

References 48 publications

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“…The problems are commonly set in terms of a minimax objective, where the maximum is taken over a class of models that is believed to contain the truth, often called the uncertainty set [19,34,4]. The use of statistical distance such as KL divergence in defining uncertainty set is particularly popular for dynamic control problems [38,28,42], economics [22,23,24], finance [9,10,17], queueing [29], and dynamic pricing [35]. In particular, [18] proposes the use of simulation, which they called robust Monte Carlo, in order to approximate the solutions for a class of worst-case optimizations that arise in finance.…”

Section: Connections To Past Literaturesmentioning

confidence: 99%

Robust Sensitivity Analysis for Stochastic Systems

2016

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We study a worst-case approach to measure the sensitivity to model misspecification in the performance analysis of stochastic systems. The situation of interest is when only minimal parametric information is available on the form of the true model. Under this setting, we post optimization programs that compute the worst-case performance measures, subject to constraints on the amount of model misspecification measured by KullbackLeibler (KL) divergence. Our main contribution is the development of infinitesimal approximations for these programs, resulting in asymptotic expansions of their optimal values in terms of the divergence. The coefficients of these expansions can be computed via simulation, and are mathematically derived from the representation of the worst-case models as changes of measure that satisfy a well-defined class of functional fixed point equations.

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Section: Connections To Past Literaturesmentioning

confidence: 99%

Robust Sensitivity Analysis for Stochastic Systems

2016

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“…Calafiore [4] proposes a methodology to optimize the worst-case risk of a portfolio (variance or absolute deviation) under distributional uncertainty characterized by KL divergence. Glasserman and Xu [14] develops portfolio control rules that are robust to distributional uncertainty. In addition to the above works, some researches pay special attention to heavy tail distributions.…”

Section: Literature Reviewmentioning

confidence: 99%

Understanding Distributional Ambiguity via Non-robust Chance Constraint

Leung

et al. 2019

SSRN Journal

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The choice of the ambiguity radius is critical when an investor uses the distributionally robust approach to address the issue that the portfolio optimization problem is sensitive to the uncertainties of the asset return distribution. It cannot be set too large because the larger the size of the ambiguity set the worse the portfolio return. It cannot be too small either; otherwise, one loses the robust protection. This tradeoff demands a financial understanding of the ambiguity set. In this paper, we propose a non-robust interpretation of the distributionally robust optimization (DRO) problem. By relating the impact of an ambiguity set to the impact of a non-robust chance constraint, our interpretation allows investors to understand the size of the ambiguity set through parameters that are directly linked to investment performance. We first show that for general φ-divergences, a DRO problem is asymptotically equivalent to a class of mean-deviation problem, where the ambiguity radius controls investor's risk preference. Based on this non-robust reformulation, we then show that when a boundedness constraint is added to the investment strategy, the DRO problem can be cast as a chance-constrained optimization (CCO) problem without distributional uncertainties. If the boundedness constraint is removed, the CCO problem is shown to perform uniformly better than the DRO problem, irrespective of the radius of the ambiguity set, the choice of the divergence measure, or the tail heaviness of the center distribution. Our results apply to both the widely-used Kullback-Leibler (KL) divergence which requires the distribution of the objective function to be exponentially bounded, as well as those more general divergence measures which allow heavy tail ones such as student t and lognormal distributions. * The corresponding author.Preprint. Under review.

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“…2 Boyd, Mueller, O'Donoghue, and Wang (2014) consider an alternative generalization of the linear quadratic case, using ideas from approximate dynamic programming. Glasserman and Xu (2013) is highly sensitive to the quadratic cost structure with linear dynamics (e.g., Bertsekas (2000)). This special case cannot handle inequality constraints on portfolio positions, nonquadratic transactions costs, or more complicated risk considerations.…”

Section: Literature Reviewmentioning

confidence: 99%

Dynamic Portfolio Choice with Linear Rebalancing Rules

Moallemi

Sağlam

2017

J. Financ. Quant. Anal.

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We consider a broad class of dynamic portfolio optimization problems that allow for complex models of return predictability, transaction costs, trading constraints, and risk considerations. Determining an optimal policy in this general setting is almost always intractable. We propose a class of linear rebalancing rules and describe an efficient computational procedure to optimize with this class. We illustrate this method in the context of portfolio execution and show that it achieves near optimal performance.We consider another numerical example involving dynamic trading with mean-variance preferences and demonstrate that our method can result in economically large benefits.

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Robust Portfolio Control with Stochastic Factor Dynamics

Cited by 21 publications

References 48 publications

Robust Sensitivity Analysis for Stochastic Systems

Robust Sensitivity Analysis for Stochastic Systems

Understanding Distributional Ambiguity via Non-robust Chance Constraint

Dynamic Portfolio Choice with Linear Rebalancing Rules

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