The Experts below are selected from a list of 23598 Experts worldwide ranked by ideXlab platform
Yan Dolinsky - One of the best experts on this subject based on the ideXlab platform.
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Continuity of Utility Maximization under weak convergence
Mathematics and Financial Economics, 2020Co-Authors: Erhan Bayraktar, Yan DolinskyAbstract:In this paper we find tight sufficient conditions for the continuity of the value of the Utility Maximization problem from terminal wealth with respect to the convergence in distribution of the underlying processes. We also establish a weak convergence result for the terminal wealths of the optimal portfolios. Finally, we apply our results to the computation of the minimal expected shortfall (shortfall risk) in the Heston model by building an appropriate lattice approximation.
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Extended Weak Convergence and Utility Maximization with Proportional Transaction Costs.
arXiv: Mathematical Finance, 2019Co-Authors: Erhan Bayraktar, Leonid Dolinskyi, Yan DolinskyAbstract:In this paper we study Utility Maximization with proportional transaction costs. Assuming extended weak convergence of the underlying processes we prove the convergence of the corresponding Utility Maximization problems. Moreover, we establish a limit theorem for the optimal trading strategies. The proofs are based on the extended weak convergence theory developed in [1] and the Meyer--Zheng topology introduced in [24].
Keita Owari - One of the best experts on this subject based on the ideXlab platform.
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On admissible strategies in robust Utility Maximization
Mathematics and Financial Economics, 2012Co-Authors: Keita OwariAbstract:The existence of optimal strategy in robust Utility Maximization is addressed when the Utility function is finite on the entire real line. A delicate problem in this case is to find a “good definition” of admissible strategies to admit an optimizer. Under certain assumptions, especially a kind of time-consistency property of the set $${\mathcal{P}}$$ of probabilities which describes the model uncertainty, we show that an optimal strategy is obtained in the class of those whose wealths are supermartingales under all local martingale measures having a finite generalized entropy with one of $${P\in\mathcal{P}}$$ .
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Robust Utility Maximization with unbounded random endowment
Advances in Mathematical Economics, 2011Co-Authors: Keita OwariAbstract:This paper studies the problem of robust Utility Maximization with random endowment. When the endowment is possibly unbounded, but satisfies certain integrability conditions, we first prove the fundamental duality relation between the Utility Maximization and the dual problem, and the existence of a solution to the dual problem. Then the existence of an optimal strategy in a certain choice of admissible class is discussed. As an application, we introduce a robust version of Utility indifference prices.
Erhan Bayraktar - One of the best experts on this subject based on the ideXlab platform.
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Continuity of Utility Maximization under weak convergence
Mathematics and Financial Economics, 2020Co-Authors: Erhan Bayraktar, Yan DolinskyAbstract:In this paper we find tight sufficient conditions for the continuity of the value of the Utility Maximization problem from terminal wealth with respect to the convergence in distribution of the underlying processes. We also establish a weak convergence result for the terminal wealths of the optimal portfolios. Finally, we apply our results to the computation of the minimal expected shortfall (shortfall risk) in the Heston model by building an appropriate lattice approximation.
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Extended Weak Convergence and Utility Maximization with Proportional Transaction Costs.
arXiv: Mathematical Finance, 2019Co-Authors: Erhan Bayraktar, Leonid Dolinskyi, Yan DolinskyAbstract:In this paper we study Utility Maximization with proportional transaction costs. Assuming extended weak convergence of the underlying processes we prove the convergence of the corresponding Utility Maximization problems. Moreover, we establish a limit theorem for the optimal trading strategies. The proofs are based on the extended weak convergence theory developed in [1] and the Meyer--Zheng topology introduced in [24].
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On the Stability of Utility Maximization Problems
arXiv: Portfolio Management, 2010Co-Authors: Erhan Bayraktar, Ross KravitzAbstract:In this paper we extend the stability results of [4]}. Our Utility Maximization problem is defined as an essential supremum of conditional expectations of the terminal values of wealth processes, conditioned on the filtration at the stopping time $\tau$. To establish our results, we extend the classical results of convex analysis to maps from $L^0$ to $L^0$. The notion of convex compactness introduced in [7] plays an important role in our analysis.
Mung Chiang - One of the best experts on this subject based on the ideXlab platform.
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Stability and benefits of suboptimal Utility Maximization
IEEE ACM Transactions on Networking, 2011Co-Authors: Tian Lan, Mung Chiang, Xiaojun Lin, Ruby B. LeeAbstract:Network Utility Maximization has been widely used to model resource allocation and network architectures. However, in practice, often it cannot be solved optimally due to complexity reasons. Thus motivated, we address the following two questions in this paper: 1) Can suboptimal Utility Maximization maintain queue stability? 2) Can underoptimization of Utility objective function in fact benefit other network design objectives? We quantify the following intuition: A resource allocation that is suboptimal with respect to a Utility Maximization formulation maintains maximum flow-level stability when the Utility gap is sufficiently small and information delay is bounded, and it can still provide a guaranteed size of stability region otherwise. Utility-suboptimal rate allocation can also enhance other network performance metrics, e.g., it may reduce link saturation. These results provide a theoretical support for turning attention from optimal but complex solutions of network optimization to those that are simple even though suboptimal.
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A tutorial on decomposition methods for network Utility Maximization
IEEE Journal on Selected Areas in Communications, 2006Co-Authors: Daniel Pérez Palomar, Mung ChiangAbstract:A systematic understanding of the decomposability structures in network Utility Maximization is key to both resource allocation and functionality allocation. It helps us obtain the most appropriate distributed algorithm for a given network resource allocation problem, and quantifies the comparison across architectural alternatives of modularized network design. Decomposition theory naturally provides the mathematical language to build an analytic foundation for the design of modularized and distributed control of networks. In this tutorial paper, we first review the basics of convexity, Lagrange duality, distributed subgradient method, Jacobi and Gauss-Seidel iterations, and implication of different time scales of variable updates. Then, we introduce primal, dual, indirect, partial, and hierarchical decompositions, focusing on network Utility Maximization problem formulations and the meanings of primal and dual decompositions in terms of network architectures. Finally, we present recent examples on: systematic search for alternative decompositions; decoupling techniques for coupled objective functions; and decoupling techniques for coupled constraint sets that are not readily decomposable
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network Utility Maximization with nonconcave utilities using sum of squares method
Conference on Decision and Control, 2005Co-Authors: Maryam Fazel, Mung ChiangAbstract:The Network Utility Maximization problem has recently been used extensively to analyze and design distributed rate allocation in networks such as the Internet. A major limitation in the state-of-the-art is that user Utility functions are assumed to be strictly concave functions, modeling elastic flows. Many applications require inelastic flow models where nonconcave Utility functions need to be maximized. It has been an open problem to find the globally optimal rate allocation that solves nonconcave network Utility Maximization, which is a difficult nonconvex optimization problem. We provide a centralized algorithm for off-line analysis and establishment of a performance benchmark for nonconcave Utility Maximization. Based on the semialgebraic approach to polynomial optimization, we employ convex sum-of-squares relaxations solved by a sequence of semidefinite programs, to obtain increasingly tighter upper bounds on total achievable Utility for polynomial utilities. Surprisingly, in all our experiments, a very low order and often a minimal order relaxation yields not just a bound on attainable network Utility, but the globally maximized network Utility. When the bound is exact, which can be proved using a sufficient test, we can also recover a globally optimal rate allocation. In addition to polynomial utilities, sigmoidal utilities can be transformed into polynomials and are handled. Furthermore, using two alternative representation theorems for positive polynomials, we present price interpretations in economics terms for these relaxations, extending the classical interpretation of independent congestion pricing on each link to pricing for the simultaneous usage of multiple links.
Ness B Shroff - One of the best experts on this subject based on the ideXlab platform.
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Utility Maximization for communication networks with multipath routing
IEEE Transactions on Automatic Control, 2006Co-Authors: Ness B ShroffAbstract:In this paper, we study Utility Maximization problems for communication networks where each user (or class) can have multiple alternative paths through the network. This type of multi-path Utility Maximization problems appear naturally in several resource allocation problems in communication networks, such as the multi-path flow control problem, the optimal quality-of-service (QoS) routing problem, and the optimal network pricing problem. We develop a distributed solution to this problem that is amenable to online implementation. We analyze the convergence of our algorithm in both continuous-time and discrete-time, and with and without measurement noise. These analyses provide us with guidelines on how to choose the parameters of the algorithm to ensure efficient network control.
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Utility Maximization for Communication Networks
2006Co-Authors: Xiaojun Lin, Ness B ShroffAbstract:In this paper, we study Utility Maximization problems for communication networks where each user (or class) can have multiple alternative paths through the network. This type of multi- path Utility Maximization problems appear naturally in several re- source allocation problems in communication networks, such as the multi-path flow control problem, the optimal quality-of-service (QoS) routing problem, and the optimal network pricing problem. We develop a distributed solution to this problem that is amenable to online implementation. We analyze the convergence of our al- gorithm in both continuous-time and discrete-time, and with and without measurement noise. These analyses provide us with guide- lines on how to choose the parameters of the algorithm to ensure efficient network control.
