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作者：Guasoni, Paolo; Robertson, Scott
作者单位：Boston University; Dublin City University; Carnegie Mellon University
摘要：This paper develops a method to derive optimal portfolios and risk premia explicitly in a general diffusion model for an investor with power utility and a long horizon. The market has several risky assets and is potentially incomplete. Investment opportunities are driven by, and partially correlated with, state variables which follow an autonomous diffusion. The framework nests models of stochastic interest rates, return predictability, stochastic volatility and correlation risk. In models wit...
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作者：Shah, Devavrat; Shin, Jinwoo
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：There has recently been considerable interest in design of low-complexity, myopic, distributed and stable scheduling algorithms for constrained queueing network models that arise in the context of emerging communication networks. Here we consider two representative models. One, a queueing network model that captures randomly varying number of packets in the queues present at a collection of wireless nodes communicating through a shared medium. Two, a buffered circuit switched network model for...
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作者：Gloria, Antoine; Otto, Felix
作者单位：Max Planck Society
摘要：This paper is the companion article to [Ann. Probab. 39 (2011) 779-856]. We consider a discrete elliptic equation on the d-dimensional lattice Z(d) with random coefficients A of the simplest type: They are identically distributed and independent from edge to edge. On scales large w.r.t. the lattice spacing (i.e., unity), the solution operator is known to behave like the solution operator of a (continuous) elliptic equation with constant deterministic coefficients. This symmetric homogenized ma...
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作者：Bhamidi, Shankar; van der Hofstad, Remco
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Eindhoven University of Technology
摘要：In the recent past, there has been a concerted effort to develop mathematical models for real-world networks and to analyze various dynamics on these models. One particular problem of significant importance is to understand the effect of random edge lengths or costs on the geometry and flow transporting properties of the network. Two different regimes are of great interest, the weak disorder regime where optimality of a path is determined by the sum of edge weights on the path and the strong d...
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作者：Knispel, Thomas
作者单位：Leibniz University Hannover
摘要：For a stochastic factor model we maximize the long-term growth rate of robust expected power utility with parameter lambda epsilon (0, 1). Using duality methods the problem is reformulated as an infinite time horizon, risk-sensitive control problem. Our results characterize the optimal growth rate, an optimal long-term trading strategy and an asymptotic worst-case model in terms of an ergodic Bellman equation. With these results we propose a duality approach to a robust large deviations criter...
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作者：Ata, Baris; Gurvich, Itai
作者单位：Northwestern University
摘要：We consider optimal control of a multi-class queue in the Halfin-Whitt regime, and revisit the notion of asymptotic optimality and the associated optimality gaps. The existing results in the literature for such systems provide asymptotically optimal controls with optimality gaps of o(root n) where n is the system size, for example, the number of servers. We construct a sequence of asymptotically optimal controls where the optimality gap grows logarithmically with the system size. Our analysis ...
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作者：Shah, Devavrat; Wischik, Damon
作者单位：Massachusetts Institute of Technology (MIT); University of London; University College London
摘要：We consider a queueing network in which there are constraints on which queues may be served simultaneously; such networks may be used to model input-queued switches and wireless networks. The scheduling policy for such a network specifies which queues to serve at any point in time. We consider a family of scheduling policies, related to the maximum-weight policy of Tassiulas and Ephremides [IEEE Trans. Automat. Control 37 (1992) 1936-1948], for single-hop and multihop networks. We specify a fl...
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作者：Kabluchko, Zakhar
作者单位：Ulm University
摘要：We prove empirical central limit theorems for the distribution of levels of various random fields defined on high-dimensional discrete structures as the dimension of the structure goes to infinity. The random fields considered include costs of assignments. weights of Hamiltonian cycles and spanning trees, energies of directed polymers, locations of particles in the branching random walk, as well as energies in the Sherrington-Kirkpatrick and Edwards-Anderson models. The distribution of levels ...
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作者：Nutz, Marcel
作者单位：Columbia University
摘要：We study utility maximization for power utility random fields with and without intermediate consumption in a general semimartingale model with closed portfolio constraints. We show that any optimal strategy leads to a solution of the corresponding Bellman equation. The optimal strategies are described pointwise in terms of the opportunity process, which is characterized as the minimal solution of the Bellman equation. We also give verification theorems for this equation.
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作者：Imkeller, Peter; Reveillac, Anthony; Richter, Anja
作者单位：Humboldt University of Berlin
摘要：In this paper we consider a class of BSDEs with drivers of quadratic growth, on a stochastic basis generated by continuous local martingales. We first derive the Markov property of a forward-backward system (FBSDE) if the generating martingale is a strong Markov process. Then we establish the differentiability of a FBSDE with respect to the initial value of its forward component. This enables us to obtain the main result of this article, namely a representation formula for the control componen...
