-
作者：Cohen, Asaf; Sun, Chuhao
作者单位：University of Michigan System; University of Michigan
摘要：In this paper, we examine the stationary relaxed singular control problem within a multidimensional framework for a single agent as well as its mean field game equivalent. We demonstrate that optimal relaxed controls exist for two problem classes: one driven by queueing control and the other by harvesting models. These relaxed controls are defined by random measures across the state and control spaces with the state process described as a solution to the associated martingale problem. By lever...
-
作者：Sanita, Laura; Verberk, Lucy
作者单位：Bocconi University; Eindhoven University of Technology
摘要：Capacitated network bargaining games are popular combinatorial games that involve the structure of matchings in graphs. We show that it is always possible to stabilize unit weight instances of this problem (that is, ensure that they admit a stable outcome) via capacity reduction and edge removal operations without decreasing the total value that the players can get. Furthermore, for general weighted instances, we show that computing a minimum amount of vertex capacity to reduce to make an inst...
-
作者：Liu, Wei; Lin, Qihang; Xu, Yangyang
作者单位：Rensselaer Polytechnic Institute; University of Iowa
摘要：Many recent studies on first-order methods (FOMs) focus on composite nonconvex nonsmooth optimization with linear and/or nonlinear function constraints. Upper (or worst-case) complexity bounds have been established for these methods. However, little can be claimed about their optimality, as no lower bound is known except for a few special smooth nonconvex cases. In this paper, we make the first attempt to establish lower complexity bounds of FOMs for solving a class of composite nonconvex nons...
-
作者：Kijima, Shuji; Shimizu, Nobutaka; Shiraga, Takeharu
作者单位：Shiga University; Chuo University
摘要：Real networks are often dynamic. In response to it, analyses of algorithms on dynamic networks attract more and more attention in network science and engineering. Random walks on dynamic graphs have also been actively investigated for over a decade, where in most cases the edge set changes but the vertex set is static. The vertex sets are also dynamic in many real networks. Motivated by the setting of random walks on growing networks, this paper introduces a simple model of graphs with an incr...
-
作者：Xing, Jie; Ma, Jingtang; Zheng, Harry
作者单位：Guizhou University of Finance & Economics; Southwestern University of Finance & Economics - China; Imperial College London
摘要：In this paper, we study a finite horizon optimal investment stopping problem with an unobservable random variable for the return of a risky asset. Using the Bayesian filter and the dual control approach, we transform the original primal problem into a dual finite horizon optimal stopping problem, which results in the dual value function satisfying a variational inequality with two state variables. For a class of utility functions that includes power utility and non-hyperbolic absolute risk ave...
-
作者：Boros, Endre; Lee, Joonhee
作者单位：Rutgers University System; Rutgers University New Brunswick; Rutgers University System; Rutgers University New Brunswick; Pace University
摘要：Hailperin (1965) introduced a linear programming formulation to a difficult family of problems, originally proposed by Boole (1854, 1868). Hailperin's model is computationally still difficult and involves an exponential number of variables (in terms of a typical input size for Boole's problem). Numerous papers provided efficiently computable bounds for the minimum and maximum values of Hailperin's model by using aggregation that is a monotone linear mapping to a lower dimensional space. In man...
-
作者：Perez, Jose Luis; Rodosthenous, Neofytos; Yamazaki, Kazutoshi
作者单位：CIMAT - Centro de Investigacion en Matematicas; University of London; University College London; University of Queensland
摘要：We introduce a new nonzero-sum game of optimal stopping with asymmetric exercise opportunities. Given a stochastic process modeling the value of an asset, one player observes and can act on the process continuously, whereas the other player can act on it only periodically at independent Poisson arrival times. The first one to stop receives a reward, different for each player, whereas the other one gets nothing. We study how each player balances the maximization of gains against the maximizatio...
-
作者：Yang, Zhou; Li, Danping; Zeng, Yan; Liu, Guanting
作者单位：South China Normal University; East China Normal University; Sun Yat Sen University; University of New South Wales Sydney
摘要：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 alpha-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 maximi...
-
作者：Callegaro, Giorgia; Di Tella, Paolo; Ongarato, Beatrice; Sgarra, Carlo
作者单位：University of Padua; Technische Universitat Dresden; Universita degli Studi di Bari Aldo Moro
摘要：The aim of this paper is to investigate a quadratic, that is, variance-optimal, semistatic hedging problem in an incomplete market model where the underlying log-asset price is driven by a diffusion process with stochastic volatility and a self-exciting jump process of the Hawkes type. More precisely, we aim at hedging a claim at time T > 0 by using a portfolio of available contingent claims so as to minimize the variance of the residual hedging error at time T. In order to improve the replica...
-
作者：Wu, Manxi; Amin, Saurabh; Ozdaglar, Asuman
作者单位：Cornell University; Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：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 payoffrelevant 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 ...
