Robust Asset Allocation with Benchmarked Objectives

Lim, Andrew; Shanthikumar, J. George; Watewai, Thaisiri

doi:10.2139/ssrn.931989

Cited by 7 publications

(7 citation statements)

References 46 publications

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“…The penalty approach, which we are using, has been widely adopted in the robust control literature (e.g., Jacobson 1973;Whittle 1981Whittle , 1990Whittle , 1991Dai Pra et al 1996;Petersen et al 2000), and has also been used in economics and operations research applications (e.g., Hansen and Sargent 2005, 2007, 2008Lim and Shanthikumar 2007;Lim et al 2012;Li and Kwon 2013). The constraint approach has been widely applied to single-stage optimization problems with parameter or moment uncertainty (e.g., Ben-Tal and Nemirovski 1998, 1999Bertsimas and Sim 2004;El Ghaoui and Lebret 1997), but has also been extended to dynamic problems with uncertainty in the model of state dynamics (e.g., Iyengar 2005, Lim et al 2011, Nilim and El Ghaoui 2005and Wiesemann et al 2013). Applications to the modeling of ambiguity-averse economic agents can be found in Schneider (2003, 2007).…”

Section: Modeling Of Ambiguitymentioning

confidence: 99%

Robust Multiarmed Bandit Problems

Kim

Lim

2016

Management Science

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T he multiarmed bandit problem is a popular framework for studying the exploration versus exploitation trade-off. Recent applications include dynamic assortment design, Internet advertising, dynamic pricing, and the control of queues. The standard mathematical formulation for a bandit problem makes the strong assumption that the decision maker has a full characterization of the joint distribution of the rewards, and that "arms" under this distribution are independent. These assumptions are not satisfied in many applications, and the outof-sample performance of policies that optimize a misspecified model can be poor. Motivated by these concerns, we formulate a robust bandit problem in which a decision maker accounts for distrust in the nominal model by solving a worst-case problem against an adversary ("nature") who has the ability to alter the underlying reward distribution and does so to minimize the decision maker's expected total profit. Structural properties of the optimal worst-case policy are characterized by using the robust Bellman (dynamic programming) equation, and arms are shown to be no longer independent under nature's worst-case response. One implication of this is that index policies are not optimal for the robust problem, and we propose, as an alternative, a robust version of the Gittins index. Performance bounds for the robust Gittins index are derived by using structural properties of the value function together with ideas from stochastic dynamic programming duality. We also investigate the performance of the robust Gittins index policy when applied to a Bayesian webpage design problem. In the presence of model misspecification, numerical experiments show that the robust Gittins index policy not only outperforms the classical Gittins index policy, but also substantially reduces the variability in the out-of-sample performance.

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Section: Modeling Of Ambiguitymentioning

confidence: 99%

Robust Multiarmed Bandit Problems

Kim

Lim

2016

Management Science

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“…In other words (8) is a partially observed stochastic control problem in which (H, y(t)) are not observable. We adopt the observable pair (x(t), S t ) as the state for (8).…”

Section: Benchmarkmentioning

confidence: 99%

“…Observe that y H (t) is a G-adapted stochastic process (for H ∈ H fixed) and y(t) is a G-adapted function valued stochastic process. The objective in (8) can be written in the form…”

Section: Benchmarkmentioning

confidence: 99%

“…One approach for dealing with robustness is the notion of relative regret (see [7], [8] and the references cited therein, and also the related notion of asymptotic regret in [5]). Relative regret is an approach to robust decision making that defines a "benchmark" for each potential value of the unknown model parameters (commonly, the optimal objective value for a decision maker who optimizes with knowledge of the true parameter values) and evaluates a decision by comparing its performance to that of the benchmark over all possible parameter values.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic portfolio choice with Bayesian regret

Chen

Lim

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

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We formulate a multi-period portfolio choice problem in which the investor is uncertain about parameters of the model, can learn these parameters over time from observing asset returns, but is also concerned about robustness. To address these concerns, we introduce an objective function which can be regarded as a Bayesian version of relative regret. The optimal portfolio is characterized and shown to involve a "tilted" posterior, where the tilting is defined in terms of a family of stochastic benchmarks. We have found this model to perform at least as well as a benchmark given the true market parameters, while outperforming it when the market assets have the same trend.

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“…El Ghaoui et al (2003) provide tractable optimization models for value-at-risk constraints under uncertain first-and second-order moment information. More recently, Lim et al (2010) develop a robust approach based on a relative benchmark objective that results in less pessimistic allocations. The use of convex risk measures in this setting has been explored as well (e.g., Lüthi and Doege 2005, Ben- Tal and Teboulle 1991 under a special class of convex risk measures known as optimized certainty equivalents; these risk measures are recently used by Natarajan et al 2010 in a distribution-robust model applied to portfolio optimization as well).…”

Section: Introductionmentioning

confidence: 99%

A Soft Robust Model for Optimization Under Ambiguity

Ben‐Tal

Bertsimas

Brown

2010

Operations Research

125

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In this paper, we propose a framework for robust optimization that relaxes the standard notion of robustness by allowing the decision maker to vary the protection level in a smooth way across the uncertainty set. We apply our approach to the problem of maximizing the expected value of a payoff function when the underlying distribution is ambiguous and therefore robustness is relevant. Our primary objective is to develop this framework and relate it to the standard notion of robustness, which deals with only a single guarantee across one uncertainty set. First, we show that our approach connects closely to the theory of convex risk measures. We show that the complexity of this approach is equivalent to that of solving a small number of standard robust problems. We then investigate the conservatism benefits and downside probability guarantees implied by this approach and compare to the standard robust approach. Finally, we illustrate the methodology on an asset allocation example consisting of historical market data over a 25-year investment horizon and find in every case we explore that relaxing standard robustness with soft robustness yields a seemingly favorable risk-return trade-off: each case results in a higher out-of-sample expected return for a relatively minor degradation of out-of-sample downside performance.

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Robust Asset Allocation with Benchmarked Objectives

Cited by 7 publications

References 46 publications

Robust Multiarmed Bandit Problems

Robust Multiarmed Bandit Problems

Dynamic portfolio choice with Bayesian regret

A Soft Robust Model for Optimization Under Ambiguity

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