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作者：Egea, Maxime; Panloup, Fabien
作者单位：Universite d'Angers; Centre National de la Recherche Scientifique (CNRS)
摘要：We propose and study a new multilevel method for the numerical approximation of a Gibbs distribution pi on Rd, 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 gamma r � gamma 02-r, r � 0,.. .,R. We first state a quantitative result under general assumptions that guarantees an epsilon-approximation (in an L2 -sense) with a co...
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作者：Attia, Luc; Oliu-Barton, Miquel; Saona, Raimundo
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Institute of Science & Technology - Austria
摘要：Zero -sum stochastic games are parameterized by payoffs, transitions, and possibly a discount rate. In this article, we study how the main solution concepts, the discounted and undiscounted values, vary when these parameters are perturbed. We focus on the marginal values, introduced by Mills in 1956 in the context of matrix games-that is, the directional derivatives of the value along any fixed perturbation. We provide a formula for the marginal values of a discounted stochastic game. Further,...
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作者：Okuno, Takayuki
作者单位：Seikei University
摘要：We study properties of the central path underlying a nonlinear semidefinite optimization problem, called an NSDP for short. The latest radical work on this topic was contributed by Yamashita and Yabe [Yamashita H, Yabe H (2012) Local and superlinear convergence of a primal-dual interior point method for nonlinear semidefinite programming. Mathematical Programming 132(1-2):1-30]: they proved that the Jacobian of a certain equation system derived from the Karush-Kuhn-Tucker (KKT) conditions of t...
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作者：Gaspard, Mallory E.; Vladimirsky, Alexander
作者单位：Cornell University; Cornell University
摘要：When traveling through a graph with an accessible deterministic path to a target, is it ever preferable to resort to stochastic node-to-node transitions instead? And, if so, what are the conditions guaranteeing that such a stochastic optimal routing policy can be computed efficiently? We aim to answer these questions here by defining a class of Opportunistically Stochastic Shortest Path (OSSP) problems and deriving sufficient conditions for applicability of noniterative label-setting methods. ...
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作者：Jezequel, Remi; Ostrovskii, Dmitrii; Gaillard, Pierre
作者单位：Inria; Universite PSL; Ecole Normale Superieure (ENS); University System of Georgia; Georgia Institute of Technology; Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Inria
摘要：In the problem of online portfolio selection as formulated by Cover [Cover TM (1991) Universal portfolios. Math. Finance 1(1):1-29], the trader repeatedly distributes the trader's capital over d assets in each of T > 1 rounds with the goal of maximizing the total return. Cover proposed an algorithm, termed universal portfolios, that performs nearly as well as the best (in hindsight) static assignment of a portfolio with an O(d log(T)) logarithmic regret. Without imposing any restrictions on th...
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作者：Zhao, Renbo
作者单位：University of Iowa
摘要：We present and analyze an away-step Frank-Wolfe method for the convex optimization problem minx is an element of Xf(Ax) + < c , x > , where f is a theta-logarithmically homogeneous self-concordant barrier, A is a linear operator that may be noninvertible, < c , > is a linear function, and X is a nonempty polytope. The applications of primary interest include D-optimal design, inference of multivariate Hawkes processes, and total variationregularized Poisson image deblurring. We establish affin...
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作者：Zhao, Lei; Zhu, Daoli; Zhang, Shuzhong
作者单位：Shanghai Jiao Tong University; Shanghai Jiao Tong University; Shanghai Jiao Tong University; The Chinese University of Hong Kong, Shenzhen; Shenzhen Research Institute of Big Data; University of Minnesota System; University of Minnesota Twin Cities
摘要：In this paper we consider a nonmonotone (mixed) variational inequality (VI) model with (nonlinear) convex conic constraints. Through developing an equivalent Lagrangian function-like primal-dual saddle point system for the VI model in question, we introduce an augmented Lagrangian primal-dual method, called ALAVI (Augmented Lagrangian Approach to Variational Inequality) in the paper, for solving a general constrained VI model. Under an assumption, called the primal-dual variational coherence c...
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作者：Herdegen, Martin; Khan, Nazem
作者单位：University of Warwick; Dublin City University
摘要：This paper revisits mean-risk portfolio selection in a one-period financial market, where risk is quantified by a star-shaped risk measure rho. We make three contributions. First, we introduce the new axiom of sensitivity to large expected losses and show that it is key to ensure the existence of optimal portfolios. Second, we give primal and dual characterizations of (strong) rho-arbitrage. Finally, we use our conditions for the absence of (strong) rho-arbitrage to explicitly derive the (stro...
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作者：Diao, Ruoyu; Dai, Yu-Hong; Zhang, Liwei
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS; Northeastern University - China; Northeastern University - China
摘要：Consider the stability properties of the Karush-Kuhn-Tucker (KKT) solution mapping SKKT for Nash equilibrium problems (NEPs) with canonical perturbations. Firstly, we obtain an exact characterization of the strong regularity of SKKT as well as an easily verified sufficient condition. Secondly, we propose equivalent conditions for the continuously differentiable single-valued localization of SKKT. Thirdly, the isolated calmness of SKKT is studied based on the I-property. The P-property is propo...
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作者：Liang, Zongxia; Xia, Jianming; Yuan, Fengyi
作者单位：Tsinghua University; Chinese Academy of Sciences; University of Michigan System; University of Michigan
摘要：This paper addresses the portfolio selection problem for nonlinear law-dependent preferences in continuous time, which inherently exhibit time inconsistency. Employing the method of the stochastic maximum principle, we establish verification theorems for equilibrium strategies, accommodating both random market coefficients and incomplete markets. We derive the first-order condition (FOC) for the equilibrium strategies, using a notion of functional derivatives with respect to probability distri...
