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作者：Shao, Hui; Zhang, Zhe George
作者单位：Zhejiang University; Western Washington University; Simon Fraser University
摘要：Extreme-case risk measures provide an approach for quantifying the upper and lower bounds of risk in situations where limited information is available regarding the underlying distributions. Previous research has demonstrated that for popular risk measures, such as value-at-risk and conditional value-at-risk, the worst-case counterparts can be evaluated in closed form when only the first two moments of the underlying distributions are known. In this study, we extend these findings by presentin...
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作者：Chaudhury, Bhaskar Ray; Garg, Jugal; Mehlhorn, Kurt; Mehta, Ruta; Misra, Pranabendu
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; Max Planck Society; University of Illinois System; University of Illinois Urbana-Champaign; Chennai Mathematical Institute
摘要：We study the problem of fairly allocating a set of indivisible goods among n agents with additive valuations. Envy freeness up to any good (EFX) is arguably the most compelling fairness notion in this context. However, the existence of an EFX allocation has not been settled and is one of the most important problems in fair division. Toward resolving this question, many impressive results show the existence of its relaxations. In particular, it is known that 0.618-EFX allocations exist and that...
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作者：Storm, Jaap; Berkelmans, Wouter; Bekker, Rene
作者单位：Eindhoven University of Technology; Vrije Universiteit Amsterdam
摘要：We consider a many-server queue in which each server can serve multiple customers in parallel. Such multitasking phenomena occur in various applications areas (e.g., in hospitals and contact centers), although the impact of the number of customers who are simultaneously served on system efficiency may vary. We establish diffusion limits of the queueing process under the quality-and-efficiency-driven scaling and for different policies of assigning customers to servers depending on the number of...
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作者：Celaya, Marcel; Kuhlmann, Stefan; Paat, Joseph; Weismantel, Robert
作者单位：Cardiff University; Technical University of Berlin; University of British Columbia
摘要：This paper deals with linear integer optimization. We develop a technique that can be applied to provide improved upper bounds for two important questions in linear integer optimization. Given an optimal vertex solution for the linear relaxation, how far away is the nearest optimal integer solution (if one exists; proximity bounds)? If a polyhedron contains no integer point, what is the smallest number of integer parallel hyperplanes defined by an integral, nonzero, normal vector that intersec...
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作者：Bolte, Jerome; Combettes, Cyrille W.; Pauwelsb, Edouard
作者单位：Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Institut Universitaire de France
摘要：The Frank-Wolfe algorithm is a popular method for minimizing a smooth convex function f over a compact convex set C. Whereas many convergence results have been derived in terms of function values, almost nothing is known about the convergence behavior of the sequence of iterates (xt)t is an element of N. Under the usual assumptions, we design several counterexamples to the convergence of (xt)t is an element of N, where f is d-time continuously differentiable, dP 2, and f(xt) -> minC f. Our cou...
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作者：Fu, Guanxing; Horst, Ulrich; Xia, Xiaonyu
作者单位：Hong Kong Polytechnic University; Hong Kong Polytechnic University; Humboldt University of Berlin; Humboldt University of Berlin; Wenzhou University
摘要：We consider a mean-field control problem with ca`dla`g semimartingale strategies arising in portfolio liquidation models with transient market impact and self-exciting order flow. We show that the value function depends on the state process only through its law, and we show that it is of linear-quadratic form and that its coefficients satisfy a coupled system of nonstandard Riccati-type equations. The Riccati equations are obtained heuristically by passing to the continuous-time limit from a s...
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作者：Kahale, Nabil
作者单位：heSam Universite; ESCP Business School
摘要：We consider a time-average estimator fk of a functional of a Markov chain. Under a coupling assumption, we show that the expectation of f(k) has a limit mu as the number of time steps goes to infinity. We describe a modification of f(k) that yields an unbiased estimator f(k) of mu. It is shown that f(k) is square integrable and has finite expected running time. Under certain conditions, f(k) can be built without any precomputations and is asymptotically at least as efficient as f(k), up to a m...
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作者：Amini, Hamed; Cao, Zhongyuan; Sulemb, Agnes
作者单位：State University System of Florida; University of Florida; Universite PSL; Universite Paris-Dauphine
摘要：We consider a general tractable model for default contagion and systemic risk in a heterogeneous financial network subjected to an exogenous macroeconomic shock. We show that under certain regularity assumptions, the default cascade model can be transformed into a death process problem represented by a balls-and-bins model. We state various limit theorems regarding the final size of default cascades. Under appropriate assumptions on the degree and threshold distributions, we prove that the fin...
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作者：Berahas, Albert S.; Curtis, Frank E.; O'Neill, Michael J.; Robinson, Daniel P.
作者单位：University of Michigan System; University of Michigan; Lehigh University; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine
摘要：A sequential quadratic optimization algorithm is proposed for solving smooth nonlinear-equality-constrained optimization problems in which the objective function is defined by an expectation. The algorithmic structure of the proposed method is based on a step decomposition strategy that is known in the literature to be widely effective in practice, wherein each search direction is computed as the sum of a normal step (toward linearized feasibility) and a tangential step (toward objective decre...
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作者：Koike, Takaaki; Lin, Liyuan; Wang, Ruodu
作者单位：Hitotsubashi University; University of Waterloo
摘要：A joint mix (JM) is a random vector with a constant component-wise sum. The dependence structure of a joint mix minimizes some common objectives, such as the variance of the component-wise sum, and it is regarded as a concept of extremal negative dependence. In this paper, we explore the connection between the joint mix structure and popular notions of negative dependence in statistics, such as negative correlation dependence, negative orthant dependence, and negative association. A joint mix ...
