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Optimization of Conditional ValueatRisk
 Journal of Risk
, 2000
"... A new approach to optimizing or hedging a portfolio of nancial instruments to reduce risk is presented and tested on applications. It focuses on minimizing Conditional ValueatRisk (CVaR) rather than minimizing ValueatRisk (VaR), but portfolios with low CVaR necessarily have low VaR as well. CVaR ..."
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Cited by 396 (26 self)
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A new approach to optimizing or hedging a portfolio of nancial instruments to reduce risk is presented and tested on applications. It focuses on minimizing Conditional ValueatRisk (CVaR) rather than minimizing ValueatRisk (VaR), but portfolios with low CVaR necessarily have low VaR as well. CVaR, also called Mean Excess Loss, Mean Shortfall, or Tail VaR, is anyway considered to be a more consistent measure of risk than VaR. Central to the new approach is a technique for portfolio optimization which calculates VaR and optimizes CVaR simultaneously. This technique is suitable for use by investment companies, brokerage rms, mutual funds, and any business that evaluates risks. It can be combined with analytical or scenariobased methods to optimize portfolios with large numbers of instruments, in which case the calculations often come down to linear programming or nonsmooth programming. The methodology can be applied also to the optimization of percentiles in contexts outside of nance.
Robust solutions to uncertain linear programs
 OR Letters
, 1999
"... We consider linear programs with uncertain parameters, lying in some prescribed uncertainty set, where part of the variables must be determined before the realization of the uncertain parameters (”nonadjustable variables”), while the other part are variables that can be chosen after the realization ..."
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Cited by 358 (15 self)
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We consider linear programs with uncertain parameters, lying in some prescribed uncertainty set, where part of the variables must be determined before the realization of the uncertain parameters (”nonadjustable variables”), while the other part are variables that can be chosen after the realization (”adjustable variables”). We extend the Robust Optimization methodology ([1, 4, 5, 6, 7, 9, 13, 14]) to this situation by introducing the Adjustable Robust Counterpart (ARC) associated with an LP of the above structure. Often the ARC is significantly less conservative than the usual Robust Counterpart (RC), however, in most cases the ARC is computationally intractable (NPhard). This difficulty is addressed by restricting the adjustable variables to be affine functions of the uncertain data. The ensuing Affinely Adjustable Robust Counterpart (AARC) problem is then shown to be, in certain important cases, equivalent to a tractable optimization problem (typically an LP or a Semidefinite problem), and in other cases, having a tight approximation which is tractable. The AARC approach is illustrated by applying it to a multistage inventory management problem.
Conditional valueatrisk for general loss distributions
 Journal of Banking and Finance
, 2002
"... Abstract. Fundamental properties of conditional valueatrisk, as a measure of risk with significant advantages over valueatrisk, are derived for loss distributions in finance that can involve discreetness. Such distributions are of particular importance in applications because of the prevalence o ..."
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Cited by 356 (28 self)
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Abstract. Fundamental properties of conditional valueatrisk, as a measure of risk with significant advantages over valueatrisk, are derived for loss distributions in finance that can involve discreetness. Such distributions are of particular importance in applications because of the prevalence of models based on scenarios and finite sampling. Conditional valueatrisk is able to quantify dangers beyond valueatrisk, and moreover it is coherent. It provides optimization shortcuts which, through linear programming techniques, make practical many largescale calculations that could otherwise be out of reach. The numerical efficiency and stability of such calculations, shown in several case studies, are illustrated further with an example of index tracking. Key Words: Valueatrisk, conditional valueatrisk, mean shortfall, coherent risk measures, risk sampling, scenarios, hedging, index tracking, portfolio optimization, risk management
PEGASUS: A policy search method for large MDPs and POMDPs
 In Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence
, 2000
"... We propose a new approach to the problem of searching a space of policies for a Markov decision process (MDP) or a partially observable Markov decision process (POMDP), given a model. Our approach is based on the following observation: Any (PO)MDP can be transformed into an "equivalent&qu ..."
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Cited by 258 (9 self)
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We propose a new approach to the problem of searching a space of policies for a Markov decision process (MDP) or a partially observable Markov decision process (POMDP), given a model. Our approach is based on the following observation: Any (PO)MDP can be transformed into an "equivalent" POMDP in which all state transitions (given the current state and action) are deterministic. This reduces the general problem of policy search to one in which we need only consider POMDPs with deterministic transitions. We give a natural way of estimating the value of all policies in these transformed POMDPs. Policy search is then simply performed by searching for a policy with high estimated value. We also establish conditions under which our value estimates will be good, recovering theoretical results similar to those of Kearns, Mansour and Ng [7], but with "sample complexity" bounds that have only a polynomial rather than exponential dependence on the horizon time. Our method appl...
The sample average approximation method for stochastic discrete optimization
 SIAM Journal on Optimization
, 2001
"... Abstract. In this paper we study a Monte Carlo simulation based approach to stochastic discrete optimization problems. The basic idea of such methods is that a random sample is generated and consequently the expected value function is approximated by the corresponding sample average function. The ob ..."
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Cited by 207 (20 self)
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Abstract. In this paper we study a Monte Carlo simulation based approach to stochastic discrete optimization problems. The basic idea of such methods is that a random sample is generated and consequently the expected value function is approximated by the corresponding sample average function. The obtained sample average optimization problem is solved, and the procedure is repeated several times until a stopping criterion is satisfied. We discuss convergence rates and stopping rules of this procedure and present a numerical example of the stochastic knapsack problem. Key words. Stochastic programming, discrete optimization, Monte Carlo sampling, Law of Large Numbers, Large Deviations theory, sample average approximation, stopping rules, stochastic knapsack problem AMS subject classifications. 90C10, 90C15
Management: Research Overview and Prospects
 Transportation Science
"... This survey reviews the fortyyear history of research on transportation revenue management (also known as yield management). We cover developments in forecasting, overbooking, seat inventory control, and pricing, as they relate to revenue management, and suggest future research directions. The surv ..."
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Cited by 150 (5 self)
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This survey reviews the fortyyear history of research on transportation revenue management (also known as yield management). We cover developments in forecasting, overbooking, seat inventory control, and pricing, as they relate to revenue management, and suggest future research directions. The survey includes a glossary of revenue management terminology and a bibliography of over 190 references. In the forty years since the first publication on overbooking control, passenger reservations systems have evolved from low level inventory control processes to major strategic information systems. Today, airlines and other transportation companies view revenue management systems and related information technologies as critical determinants of future success. Indeed, expectations of revenue gains that are possible with expanded revenue management capabilities are now driving the acquisition
Theory and applications of Robust Optimization
, 2007
"... In this paper we survey the primary research, both theoretical and applied, in the field of Robust Optimization (RO). Our focus will be on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying the most pr ..."
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Cited by 100 (14 self)
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In this paper we survey the primary research, both theoretical and applied, in the field of Robust Optimization (RO). Our focus will be on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying the most prominent theoretical results of RO over the past decade, we will also present some recent results linking RO to adaptable models for multistage decisionmaking problems. Finally, we will highlight successful applications of RO across a wide spectrum of domains, including, but not limited to, finance, statistics, learning, and engineering.
Boosted sampling: Approximation algorithms for stochastic optimization problems
 IN: 36TH STOC
, 2004
"... Several combinatorial optimization problems choose elements to minimize the total cost of constructing a feasible solution that satisfies requirements of clients. In the STEINER TREE problem, for example, edges must be chosen to connect terminals (clients); in VERTEX COVER, vertices must be chosen t ..."
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Cited by 99 (25 self)
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Several combinatorial optimization problems choose elements to minimize the total cost of constructing a feasible solution that satisfies requirements of clients. In the STEINER TREE problem, for example, edges must be chosen to connect terminals (clients); in VERTEX COVER, vertices must be chosen to cover edges (clients); in FACILITY LOCATION, facilities must be chosen and demand vertices (clients) connected to these chosen facilities. We consider a stochastic version of such a problem where the solution is constructed in two stages: Before the actual requirements materialize, we can choose elements in a first stage. The actual requirements are then revealed, drawn from a prespecified probability distribution π; thereupon, some more elements may be chosen to obtain a feasible solution for the actual requirements. However, in this second (recourse) stage, choosing an element is costlier by a factor of σ> 1. The goal is to minimize the first stage cost plus the expected second stage cost. We give a general yet simple technique to adapt approximation algorithms for several deterministic problems to their stochastic versions via the following method. • First stage: Draw σ independent sets of clients from the distribution π and apply the approximation algorithm to construct a feasible solution for the union of these sets. • Second stage: Since the actual requirements have now been revealed, augment the firststage solution to be feasible for these requirements.