Mathematics of Operations Research最新文献_第6页

Optimal Investment Strategy for α-Robust Utility Maximization Problem α-稳健效用最大化问题的最优投资策略

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-03-21 DOI: 10.1287/moor.2023.0076

Zhou Yang, Danping Li, Yan Zeng, Guanting Liu

{"title":"Optimal Investment Strategy for α-Robust Utility Maximization Problem","authors":"Zhou Yang, Danping Li, Yan Zeng, Guanting Liu","doi":"10.1287/moor.2023.0076","DOIUrl":"https://doi.org/10.1287/moor.2023.0076","url":null,"abstract":"In reality, investors are uncertain about the dynamics of risky asset returns. Therefore, investors prefer to make robust investment decisions. In this paper, we propose an α-robust utility maximization problem under uncertain parameters. The investor is allowed to invest in a financial market consisting of a risk-free asset and a risky asset. The uncertainty about the expected return rate is parameterized by a nonempty set. Different from most existing literature on robust utility maximization problems where investors are generally assumed to be extremely ambiguity averse because they tend to consider only expected utility in the worst-case scenario, we pay attention to the investors who are not only ambiguity averse but also ambiguity seeking. Under power utility, we provide the implicit function representations for the precommitted strategy, equilibrium strategy of the open-loop type, and equilibrium strategy of the closed-loop type. Some properties about the optimal trading strategies, the best-case and worst-case parameters under three different kinds of strategies, are provided.Funding: This work was supported by National Natural Science Foundation of China [Grants 12071147, 12171169, 12271171, 12371470, 71721001, 71931004, 72371256], the Shanghai Philosophy Social Science Planning Office Project [Grant 2022ZJB005], Fundamental Research Funds for the Central Universities [Grant 2022QKT001], the Excellent Young Team Project Natural Science Foundation of Guangdong Province of China [Grant 2023B1515040001], the Philosophy and Social Science Programming Foundation of Guangdong Province [Grant GD22CYJ17], the Nature Science Foundation of Guangdong Province of China [Grant 2022A1515011472], and the 111 Project [Grant B14019].","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":"183 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140199553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Multilevel Langevin Pathwise Average for Gibbs Approximation 用于吉布斯逼近的多级朗之文路径平均法

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-03-20 DOI: 10.1287/moor.2021.0243

Maxime Egéa, Fabien Panloup

{"title":"Multilevel Langevin Pathwise Average for Gibbs Approximation","authors":"Maxime Egéa, Fabien Panloup","doi":"10.1287/moor.2021.0243","DOIUrl":"https://doi.org/10.1287/moor.2021.0243","url":null,"abstract":"We propose and study a new multilevel method for the numerical approximation of a Gibbs distribution π on [Formula: see text], based on (overdamped) Langevin diffusions. This method relies on a multilevel occupation measure, that is, on an appropriate combination of R occupation measures of (constant-step) Euler schemes with respective steps [Formula: see text]. We first state a quantitative result under general assumptions that guarantees an ε-approximation (in an L2-sense) with a cost of the order [Formula: see text] or [Formula: see text] under less contractive assumptions. We then apply it to overdamped Langevin diffusions with strongly convex potential [Formula: see text] and obtain an ε-complexity of the order [Formula: see text] or [Formula: see text] under additional assumptions on U. More precisely, up to universal constants, an appropriate choice of the parameters leads to a cost controlled by [Formula: see text] (where [Formula: see text] and [Formula: see text] respectively denote the supremum and the infimum of the largest and lowest eigenvalue of [Formula: see text]). We finally complete these theoretical results with some numerical illustrations, including comparisons to other algorithms in Bayesian learning and opening to the non–strongly convex setting.Funding: The authors are grateful to the SIRIC ILIAD Nantes-Angers program, supported by the French National Cancer Institute [INCA-DGOS-Inserm Grant 12558].","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":"80 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140297973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Mean-Field Multiagent Reinforcement Learning: A Decentralized Network Approach 平均场多代理强化学习：分散网络方法

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-03-13 DOI: 10.1287/moor.2022.0055

Haotian Gu, Xin Guo, Xiaoli Wei, Renyuan Xu

{"title":"Mean-Field Multiagent Reinforcement Learning: A Decentralized Network Approach","authors":"Haotian Gu, Xin Guo, Xiaoli Wei, Renyuan Xu","doi":"10.1287/moor.2022.0055","DOIUrl":"https://doi.org/10.1287/moor.2022.0055","url":null,"abstract":"One of the challenges for multiagent reinforcement learning (MARL) is designing efficient learning algorithms for a large system in which each agent has only limited or partial information of the entire system. Whereas exciting progress has been made to analyze decentralized MARL with the network of agents for social networks and team video games, little is known theoretically for decentralized MARL with the network of states for modeling self-driving vehicles, ride-sharing, and data and traffic routing. This paper proposes a framework of localized training and decentralized execution to study MARL with the network of states. Localized training means that agents only need to collect local information in their neighboring states during the training phase; decentralized execution implies that agents can execute afterward the learned decentralized policies, which depend only on agents’ current states. The theoretical analysis consists of three key components: the first is the reformulation of the MARL system as a networked Markov decision process with teams of agents, enabling updating the associated team Q-function in a localized fashion; the second is the Bellman equation for the value function and the appropriate Q-function on the probability measure space; and the third is the exponential decay property of the team Q-function, facilitating its approximation with efficient sample efficiency and controllable error. The theoretical analysis paves the way for a new algorithm LTDE-Neural-AC, in which the actor–critic approach with overparameterized neural networks is proposed. The convergence and sample complexity are established and shown to be scalable with respect to the sizes of both agents and states. To the best of our knowledge, this is the first neural network–based MARL algorithm with network structure and provable convergence guarantee.Funding: X. Wei is partially supported by NSFC no. 12201343. R. Xu is partially supported by the NSF CAREER award DMS-2339240.","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":"30 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140147661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Semidefinite Approximations for Bicliques and Bi-Independent Pairs 双桥和双独立对的半无限逼近法

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-03-13 DOI: 10.1287/moor.2023.0046

Monique Laurent, Sven Polak, Luis Felipe Vargas

{"title":"Semidefinite Approximations for Bicliques and Bi-Independent Pairs","authors":"Monique Laurent, Sven Polak, Luis Felipe Vargas","doi":"10.1287/moor.2023.0046","DOIUrl":"https://doi.org/10.1287/moor.2023.0046","url":null,"abstract":"We investigate some graph parameters dealing with bi-independent pairs (A, B) in a bipartite graph [Formula: see text], that is, pairs (A, B) where [Formula: see text], and [Formula: see text] are independent. These parameters also allow us to study bicliques in general graphs. When maximizing the cardinality [Formula: see text], one finds the stability number [Formula: see text], well-known to be polynomial-time computable. When maximizing the product [Formula: see text], one finds the parameter g(G), shown to be NP-hard by Peeters in 2003, and when maximizing the ratio [Formula: see text], one finds h(G), introduced by Vallentin in 2020 for bounding product-free sets in finite groups. We show that h(G) is an NP-hard parameter and, as a crucial ingredient, that it is NP-complete to decide whether a bipartite graph G has a balanced maximum independent set. These hardness results motivate introducing semidefinite programming (SDP) bounds for g(G), h(G), and [Formula: see text] (the maximum cardinality of a balanced independent set). We show that these bounds can be seen as natural variations of the Lovász ϑ-number, a well-known semidefinite bound on [Formula: see text]. In addition, we formulate closed-form eigenvalue bounds, and we show relationships among them as well as with earlier spectral parameters by Hoffman and Haemers in 2001 and Vallentin in 2020.Funding: This work was supported by H2020 Marie Skłodowska-Curie Actions [Grant 813211 (POEMA)].","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":"23 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140147775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Marginal Values of a Stochastic Game 随机博弈的边际值

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-03-12 DOI: 10.1287/moor.2023.0297

Luc Attia, Miquel Oliu-Barton, Raimundo Saona

引用次数: 0

Convergence and Stability of Coupled Belief-Strategy Learning Dynamics in Continuous Games 连续博弈中信念-策略耦合学习动态的收敛性与稳定性

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-03-12 DOI: 10.1287/moor.2022.0161

Manxi Wu, Saurabh Amin, Asuman Ozdaglar

{"title":"Convergence and Stability of Coupled Belief-Strategy Learning Dynamics in Continuous Games","authors":"Manxi Wu, Saurabh Amin, Asuman Ozdaglar","doi":"10.1287/moor.2022.0161","DOIUrl":"https://doi.org/10.1287/moor.2022.0161","url":null,"abstract":"We propose a learning dynamics to model how strategic agents repeatedly play a continuous game while relying on an information platform to learn an unknown payoff-relevant parameter. In each time step, the platform updates a belief estimate of the parameter based on players’ strategies and realized payoffs using Bayes’ rule. Then, players adopt a generic learning rule to adjust their strategies based on the updated belief. We present results on the convergence of beliefs and strategies and the properties of convergent fixed points of the dynamics. We obtain sufficient and necessary conditions for the existence of globally stable fixed points. We also provide sufficient conditions for the local stability of fixed points. These results provide an approach to analyzing the long-term outcomes that arise from the interplay between Bayesian belief learning and strategy learning in games and enable us to characterize conditions under which learning leads to a complete information equilibrium.Funding: Financial support from the Air Force Office of Scientific Research [Project Building Attack Resilience into Complex Networks], the Simons Institute [research fellowship], and a Michael Hammer Fellowship is gratefully acknowledged.","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":"72 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140147400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Policy Gradient Algorithm for the Risk-Sensitive Exponential Cost MDP 风险敏感指数成本 MDP 的策略梯度算法

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-03-11 DOI: 10.1287/moor.2022.0139

Mehrdad Moharrami, Yashaswini Murthy, Arghyadip Roy, R. Srikant

{"title":"A Policy Gradient Algorithm for the Risk-Sensitive Exponential Cost MDP","authors":"Mehrdad Moharrami, Yashaswini Murthy, Arghyadip Roy, R. Srikant","doi":"10.1287/moor.2022.0139","DOIUrl":"https://doi.org/10.1287/moor.2022.0139","url":null,"abstract":"We study the risk-sensitive exponential cost Markov decision process (MDP) formulation and develop a trajectory-based gradient algorithm to find the stationary point of the cost associated with a set of parameterized policies. We derive a formula that can be used to compute the policy gradient from (state, action, cost) information collected from sample paths of the MDP for each fixed parameterized policy. Unlike the traditional average cost problem, standard stochastic approximation theory cannot be used to exploit this formula. To address the issue, we introduce a truncated and smooth version of the risk-sensitive cost and show that this new cost criterion can be used to approximate the risk-sensitive cost and its gradient uniformly under some mild assumptions. We then develop a trajectory-based gradient algorithm to minimize the smooth truncated estimation of the risk-sensitive cost and derive conditions under which a sequence of truncations can be used to solve the original, untruncated cost problem.Funding: This work was supported by the Office of Naval Research Global [Grant N0001419-1-2566], the Division of Computer and Network Systems [Grant 21-06801], the Army Research Office [Grant W911NF-19-1-0379], and the Division of Computing and Communication Foundations [Grants 17-04970 and 19-34986].","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":"7 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140107747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Parametric Semidefinite Programming: Geometry of the Trajectory of Solutions 参数半无限编程：解的轨迹几何

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-03-08 DOI: 10.1287/moor.2021.0097

Antonio Bellon, Didier Henrion, Vyacheslav Kungurtsev, Jakub Mareček

引用次数: 0

On the (Im-)Possibility of Representing Probability Distributions as a Difference of I.I.D. Noise Terms 论以 I.I.D. 噪声项之差表示概率分布的（非）可能性

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-03-07 DOI: 10.1287/moor.2023.0081

Christian Ewerhart, Marco Serena

引用次数: 0

Optimal Consumption and Investment with Independent Stochastic Labor Income 具有独立随机劳动收入的最优消费与投资

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-03-05 DOI: 10.1287/moor.2023.0119

Alain Bensoussan, Seyoung Park

{"title":"Optimal Consumption and Investment with Independent Stochastic Labor Income","authors":"Alain Bensoussan, Seyoung Park","doi":"10.1287/moor.2023.0119","DOIUrl":"https://doi.org/10.1287/moor.2023.0119","url":null,"abstract":"We develop a new dynamic continuous-time model of optimal consumption and investment to include independent stochastic labor income. We reduce the problem of solving the Bellman equation to a problem of solving an integral equation. We then explicitly characterize the optimal consumption and investment strategy as a function of income-to-wealth ratio. We provide some analytical comparative statics associated with the value function and optimal strategies. We also develop a quite general numerical algorithm for control iteration and solve the Bellman equation as a sequence of solutions to ordinary differential equations. This numerical algorithm can be readily applied to many other optimal consumption and investment problems especially with extra nondiversifiable Brownian risks, resulting in nonlinear Bellman equations. Finally, our numerical analysis illustrates how the presence of stochastic labor income affects the optimal consumption and investment strategy.Funding: A. Bensoussan was supported by the National Science Foundation under grant [DMS-2204795]. S. Park was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea, South Korea [NRF-2022S1A3A2A02089950].","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":"278 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140055887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0