Mathematics of Operations Research

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• Gaussian Limits for a Fork-Join Network with Nonexchangeable Synchronization in Heavy Traffic AI翻译
  作者：Lu, Hongyuan; Pang, Guodong
  作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
  摘要：We study a fork-join network of stations with multiple servers and nonexchangeable synchronization in heavy traffic under the first-come-first-served (FCFS) discipline. Tasks are only synchronized if all the tasks associated with the same job are completed. Service times of parallel tasks of each job can be correlated. We jointly consider the number of tasks in each waiting buffer for synchronization with the number of tasks in each parallel service station and the number of synchronized jobs....
• Convergence Analysis for Distributionally Robust Optimization and Equilibrium Problems AI翻译
  作者：Sun, Hailin; Xu, Huifu
  作者单位：Harbin Institute of Technology; Nanjing University of Science & Technology; University of Southampton
  摘要：In this paper, we study distributionally robust optimization approaches for a one-stage stochastic minimization problem, where the true distribution of the underlying random variables is unknown but it is possible to construct a set of probability distributions, which contains the true distribution and optimal decision is taken on the basis of the worst-possible distribution from that set. We consider the case when the distributional set (which is also known as the ambiguity set) varies and it...
• Diffusion Limit of Fair Resource Control-Stationarity and Interchange of Limits AI翻译
  作者：Ye, Heng-Qing; Yao, David D.
  作者单位：Hong Kong Polytechnic University; Columbia University
  摘要：We study a resource-sharing network where each job requires the concurrent occupancy of a subset of links (servers/resources), and each link's capacity is shared among job classes that require its service. The real-time allocation of the service capacity among job classes is determined by the so-called proportional fair scheme, which allocates the capacity among job classes taking into account the queue lengths and the shadow prices of link capacity. We show that the usual traffic condition is...
• Multivariate Transient Price Impact and Matrix-Valued Positive Definite Functions AI翻译
  作者：Alfonsi, Aurelien; Kloeck, Florian; Schied, Alexander
  作者单位：Institut Polytechnique de Paris; Ecole des Ponts ParisTech; Universite Gustave-Eiffel; University of Mannheim
  摘要：We consider a model for linear transient price impact for multiple assets that takes cross-asset impact into account. Our main goal is to single out properties that need to be imposed on the decay kernel so that the model admits well-behaved optimal trade execution strategies. We first show that the existence of such strategies is guaranteed by assuming that the decay kernel corresponds to a matrix-valued positive definite function. An example illustrates, however, that positive definiteness a...
• Fundamental Theorem of Asset Pricing Under Transaction Costs and Model Uncertainty AI翻译
  作者：Bayraktar, Erhan; Zhang, Yuchong
  作者单位：University of Michigan System; University of Michigan; Columbia University
  摘要：We prove the fundamental theorem of asset pricing for a discrete time financial market where trading is subject to proportional transaction costs and the asset price dynamic is modeled by a family of probability measures, possibly nondominated. Using a backward-forward scheme, we show that when the market consists of a money market account and a single stock, no-arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of consistent price systems. We also show that wh...
• Robust Polynomial-Time Approximation Schemes for Parallel Machine Scheduling with Job Arrivals and Departures AI翻译
  作者：Skutella, Martin; Verschae, Jose
  作者单位：Technical University of Berlin; Pontificia Universidad Catolica de Chile
  摘要：Scheduling a set of n jobs on m identical parallel machines so as to minimize the makespan or maximize the minimum machine load are two of the most important and fundamental scheduling problems studied in the literature. We consider the general online scenario where jobs are consecutively added to and/or deleted from an instance. The goal is to maintain a near-optimal assignment of the current set of jobs to the m machines. This goal is essentially doomed to failure unless, upon arrival or dep...
• Convex Duality in Stochastic Optimization and Mathematical Finance (vol 36, pg 340, 2011) AI翻译
  作者：Pennanen, Teemu
  作者单位：University of London; King's College London
  摘要：In Pennanen [2] [Pennanen T (2011) Convex duality in stochastic optimization and mathematical finance. Math. Oper. Res. 36(2):340-362], Theorem 2.2 is not valid as stated. It omits certain integrability conditions that are needed in general. The additional conditions are satisfied in most of the applications given in Pennanen [2]. For the remaining ones, sufficient conditions are given below. The topological results in Section 5 remain unaffected. A corrected version is given.
• Holder-Like Property and Metric Regularity of a Positive-Order for Implicit Multifunctions AI翻译
  作者：Thai Doan Chuong; Do Sang Kim
  作者单位：Saigon University; Pukyong National University
  摘要：We introduce concepts of metric regularity and metric subregularity of a positive-order for an implicit multifunction and provide new sufficient conditions for the implicit multifunctions to achieve the addressed properties. The conditions provided are presented in terms of the Frechet/Mordukhovich coderivative of the corresponding parametric multifunction formulated the implicit multifunction. We show that such sufficient conditions are also necessary for the metric regularity/subregularity o...
• Convexity and Solutions of Stochastic Multidimensional 0-1 Knapsack Problems with Probabilistic Constraints AI翻译
  作者：Yoda, Kunikazu; Prekopa, Andras
  作者单位：Rutgers University System; Rutgers University New Brunswick
  摘要：In the multidimensional 0-1 knapsack problem, we are given a set of items, each with a value and multiple attributes, and we want to select a subset in such a way that the total value is maximized while the total quantity of each attribute satisfies a capacity constraint. In this paper, we assume that quantities of the item attributes are independent random variables such that those of the same attribute across different items follow the same type of probability distribution, not necessarily w...
• Maximization of Nonconcave Utility Functions in Discrete-Time Financial Market Models AI翻译
  作者：Carassus, Laurence; Rasonyi, Miklos
  作者单位：Universite de Reims Champagne-Ardenne; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Universite Paris Cite; University of Edinburgh
  摘要：This paper investigates the problem of maximizing expected terminal utility in a (generically incomplete) discrete-time financial market model with finite time horizon. By contrast to the standard setting, a possibly nonconcave utility function U is considered, with domain of definition equal to the whole real line. Simple conditions are presented that guarantee the existence of an optimal strategy for the problem. In particular, the asymptotic elasticity of U plays a decisive role: Existence ...