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Pricing American options: a duality approach.
 Operation Research
, 2004
"... Abstract We develop a new method for pricing American options. The main practical contribution of this paper is a general algorithm for constructing upper and lower bounds on the true price of the option using any approximation to the option price. We show that our bounds are tight, so that if the ..."
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Cited by 147 (6 self)
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Abstract We develop a new method for pricing American options. The main practical contribution of this paper is a general algorithm for constructing upper and lower bounds on the true price of the option using any approximation to the option price. We show that our bounds are tight, so that if the initial approximation is close to the true price of the option, the bounds are also guaranteed to be close. We also explicitly characterize the worstcase performance of the pricing bounds. The computation of the lower bound is straightforward and relies on simulating the suboptimal exercise strategy implied by the approximate option price. The upper bound is also computed using Monte Carlo simulation. This is made feasible by the representation of the American option price as a solution of a properly defined dual minimization problem, which is the main theoretical result of this paper. Our algorithm proves to be accurate on a set of sample problems where we price call options on the maximum and the geometric mean of a collection of stocks. These numerical results suggest that our pricing method can be successfully applied to problems of practical interest.
Duality Approaches to Economic LotSizing Games
, 2007
"... We consider the economic lotsizing (ELS) game with general concave ordering cost. In this cooperative game, multiple retailers form a coalition by placing joint orders to a single supplier in order to reduce ordering cost. When both the inventory holding cost and backlogging cost are linear functio ..."
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Cited by 7 (3 self)
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functions, it can be shown that the core of this game is nonempty. The main contribution of this paper is to show that a core allocation can be computed in polynomial time. Our approach is based on linear programming (LP) duality and is motivated by the work of Owen [19]. We suggest an integer programming
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 819 (28 self)
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of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
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Cited by 547 (12 self)
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We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized
Optimal Investments for Risk and AmbiguityAverse Preferences: A Duality Approach
, 2006
"... Ambiguity, also called Knightian or model uncertainty, is a key feature in financial modeling. A recent paper by Maccheroni et al. (2004) characterizes investor preferences under aversion against both risk and ambiguity. Their result shows that these preferences can be numerically represented in te ..."
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Cited by 39 (8 self)
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in terms of convex risk measures. In this paper we study the corresponding problem of optimal investment over a given time horizon, using a duality approach and building upon the results by Kramkov and Schachermayer (1999, 2001).
A DUALITY APPROACH TO THE FRACTIONAL LAPLACIAN WITH MEASURE DATA
"... Abstract. We describe a duality method to prove both existence and uniqueness of solutions to nonlocal problems like (−∆) s v = µ in R N, with vanishing conditions at infinity. Here µ is a bounded Radon measure whose support is compactly contained in R N, N ≥ 2, and −(∆) s is the fractional Laplace ..."
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Cited by 8 (1 self)
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Abstract. We describe a duality method to prove both existence and uniqueness of solutions to nonlocal problems like (−∆) s v = µ in R N, with vanishing conditions at infinity. Here µ is a bounded Radon measure whose support is compactly contained in R N, N ≥ 2, and −(∆) s is the fractional Laplace
A Duality Approach to Path Planning for Multiple Robots †
"... Abstract — In this paper, we propose an optimizationbased framework for path planning for multiple robots in presence of obstacles. The objective is to find multiple fixed length paths for multiple robots that satisfy the following constraints: (i) bounded curvature, (ii) obstacle avoidance, (iii) ..."
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Cited by 1 (0 self)
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coverage, can be cast as a nonconvex optimization problem. Then, we propose an alternative dual formulation that results in no duality gap. We show that the alternative dual function can be interpreted as minimum potential energy of a multiparticle system with discontinuous springlike forces. Finally, we
A Duality Approach in the Optimization of Beams and Plates
, 1997
"... We introduce a class of nonlinear transformations called "resizing rules" which associate to optimal shape design problems certain equivalent distributed control problems, while preserving the state of the system. This puts into evidence the duality principle that the class of system state ..."
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Cited by 3 (1 self)
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We introduce a class of nonlinear transformations called "resizing rules" which associate to optimal shape design problems certain equivalent distributed control problems, while preserving the state of the system. This puts into evidence the duality principle that the class of system
Results 1  10
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