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作者：Christodoulou, George; Fiat, Amos; Koutsoupias, Elias; Sgouritsa, Alkmini
作者单位：Aristotle University of Thessaloniki; Tel Aviv University; University of Oxford; Athens University of Economics & Business
摘要：We study envy-freeness up to any good (EFX) in settings where valuations can be represented via a graph of arbitrary size where vertices correspond to agents and edges to items. An item (edge) has zero marginal value to all agents (vertices) not incident to the edge. Each vertex may have an arbitrary monotone valuation on the set of incident edges. We first consider allocations that correspond to orientations of the edges, where we show that EFX does not always exist, and furthermore, that it ...
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作者：Cerny, Ales; Ruf, Johannes; Schweizer, Martin
作者单位：University of London; London School Economics & Political Science; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Monotone mean-variance (MMV) utility is the minimal modification of the classical Markowitz mean-variance (MV) utility that respects rational ordering of investment opportunities. This paper provides, for the first time, a complete characterization of optimal dynamic portfolio choice for the MMV utility in asset price models with independent returns. The task is performed under minimal assumptions, weaker than the existence of an equivalent martingale measure and with no restrictions on the mo...
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作者：Olikier, Guillaume; Gallivan, Kyle A.; Absil, P. -A.
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; State University System of Florida; Florida State University; Universite Catholique Louvain
摘要：This paper considers the problem of minimizing a differentiable function with locally Lipschitz continuous gradient on the algebraic variety of real matrices of upperbounded rank. This problem is known to enable the formulation of various machine learning or signal processing tasks such as dimensionality reduction, collaborative filtering, and signal recovery. Several definitions of stationarity exist for this nonconvex problem. Among them, Bouligand stationarity is the strongest necessary con...
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作者：Renaud, Jean-Francois; Roch, Alexandre; Simard, Clarence
作者单位：University of Quebec; University of Quebec Montreal; University of Quebec; University of Quebec Montreal
摘要：We study an optimal stochastic control problem in which a firm's cash/surplus process is controlled by dividend payments and capital injections. We consider absolutely continuous dividend policies subject to a level-dependent upper bound on the dividend rate and general capital injection strategies. We construct an optimal solution for which either the optimal capital injections consist of a forced bailout strategy when the cash process reaches zero or no injection of capital is ever made and ...
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作者：Baas, Stef; Boucherie, Richard J.; Braaksma, Aleida
作者单位：University of Twente
摘要：A sampling-based method is introduced to approximate the Gittins index for a general family of alternative bandit processes. The approximation consists of a truncation of the optimization horizon and support for the immediate rewards, an optimal stopping value approximation, and a stochastic approximation procedure. Finite-time error bounds are given for the three approximations, leading to a procedure to construct a confidence interval for the Gittins index using a finite number of Monte Carl...
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作者：Backhoff-Veraguas, Julio; Zhang, Xin
作者单位：University of Vienna; New York University; New York University Tandon School of Engineering
摘要：Defining a divergence between the laws of continuous martingales is a delicate task, owing to the fact that these laws tend to be singular to each other. An important idea, by Gantert, is to instead consider a scaling limit of the relative entropy between such continuous martingales sampled over a finite time grid. This gives rise to the concept of specific relative entropy. In order to develop a general theory of divergences between continuous martingales, it is natural to replace the role of...
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作者：Guo, Feng; Wang, Jie; Zheng, Jianhao
作者单位：Dalian University of Technology; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：This paper is devoted to the problem of minimizing a sum of rational functions over a basic semialgebraic set. We provide a hierarchy of sum-of-squares (SOS) relaxations that is dual to the generalized moment problem approach proposed by Bugarin, Henrion, and Lasserre. The investigation of the dual SOS aspect offers two benefits: (1) it allows us to conduct a convergence rate analysis for the hierarchy; (2) it leads to a sign symmetry-adapted hierarchy consisting of block-diagonal semidefinite...
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作者：Atar, Rami; Ichiba, Tomoyuki
作者单位：Technion Israel Institute of Technology; University of California System; University of California Santa Barbara
摘要：Banerjee, Budhiraja and Estevez (2025) studied a randomized load balancing model in a heavy traffic asymptotic regime where the load balancing stream is thin compared to the total arrival stream. It was shown that the limit is given by a system of rankbased Brownian particles on the half-line. In this paper we extend this result from the case of exponential service time to an invariance principle, where service times have finite second moment. The main tool is a new notion of rank-based stocha...
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作者：Kavitha, Telikepalli; Makino, Kazuhisa
作者单位：Tata Institute of Fundamental Research (TIFR); Tata Institute of Fundamental Research (TIFR), Mumbai; Kyoto University
摘要：We consider a matching problem in a hospitals/residents instance G, that is, a many-to-one matching instance, in which every vertex has a strict ranking of its neighbors and hospitals have capacities. A matching M is said to be popular if M does not lose an election against any matching in which vertices cast votes for one matching versus another. There are efficient algorithms to find popular matchings in G, but it is NP-hard to find a min-cost popular matching when edges have costs. When pre...
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作者：Yu, Di; Henderson, Shane G.; Pasupathy, Raghu
作者单位：Purdue University System; Purdue University; Cornell University
摘要：Motivated by applications in emergency response and experimental design, we consider smooth stochastic optimization problems over probability measures supported on compact subsets of the Euclidean space. With the influence function as the variational object, we construct a deterministic Frank-Wolfe (dFW) recursion for probability spaces. The dFW recursion is made especially possible by a lemma that identifies the solution to the infinite-dimensional Frank-Wolfe subproblem as a Dirac measure co...
