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We describe a general technique for determining upper bounds on maximal values (or lower bounds on minimal costs) in stochastic dynamic programs. In this approach, we relax the nonanticipativity constraints that require decisions to depend only on the information available at the time a decision is made and impose a " penalty " that punishes violations of(More)
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(More)
We consider the problem of dynamic portfolio optimization in a discrete-time, finite-horizon setting. Our general model considers risk aversion, portfolio constraints (e.g., no short positions), return predictability, and transaction costs. This problem is naturally formulated as a stochastic dynamic program. Unfortunately, with non-zero transaction costs,(More)
In this paper, we propose a methodology for constructing uncertainty sets within the framework of robust optimization for linear optimization problems with uncertain parameters. Our approach relies on decision-maker risk preferences. Specifically, we utilize the theory of coherent risk measures initiated by Artzner et al. [3], and show that such risk(More)
This paper was motivated by the problem of developing an optimal strategy for exploring a large oil and gas field in the North Sea. Where should we drill first? Where do we drill next? The problem resembles a classical multiarmed bandit problem, but probabilistic dependence plays a key role: outcomes at drilled sites reveal information about neighboring(More)
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(More)
We analyze the problem of an investor who needs to unwind a portfolio in the face of recurring and uncertain liquidity needs, with a model that accounts for both permanent and temporary price impact of trading. We first show that a risk-neutral investor who myopically deleverages his position to meet an immediate need for cash always prefers to sell more(More)
—Despite the celebrated success of dynamic programming for optimizing quadratic cost functions over linear systems, such an approach is limited by its inability to tractably deal with even simple constraints. In this paper, we present an alternative approach based on results from robust optimization to solve the stochastic linear-quadratic control (SLQC)(More)
Standard andrology tests do not predict fertility or assess the genetic quality of spermatozoa. To address these problems, we have analyzed sperm nuclear activation in vitro using cytoplasmic extracts of Xenopus laevis frog eggs. The objective of this study was to determine if rat sperm chemically damaged in vivo by cyclophosphamide treatment would respond(More)