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作者：Assumpcao, Henrique; Coutinho, Gabriel
作者单位：Universidade Federal de Minas Gerais
摘要：We use semidefinite programming to bound the fractional cut-cover parameter of graphs in association schemes in terms of their smallest eigenvalue. We also extend the equality cases of a primal-dual inequality involving the Goemans-Williamson semidefinite program, which approximates MAXCUT, to graphs in certain coherent configurations. Moreover, we obtain spectral bounds for MAX 2-SAT when the underlying graphs belong to an association scheme by means of a certain semidefinite program used to ...
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作者：Kim, Takwon; Yang, Zhou; Jeon, Junkee
作者单位：Sungshin Women's University; South China Normal University; Kyung Hee University
摘要：This paper investigates an optimal consumption, investment, and early retirement problem in the presence of a mandatory retirement date and a borrowing constraint that prohibits borrowing against future labor income during employment. To handle the borrowing constraint, we employ a dual-martingale approach and reformulate the problem as a finite-horizon, two-player, zero-sum game between a singular controller and a stopper. The value of the game is characterized by a parabolic variational ineq...
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作者：Kahale, Nabil
作者单位：heSam Universite; ESCP Business School
摘要：We consider an online least squares regression problem with optimal solution u' and Hessian matrix H, and study a time-average stochastic gradient descent estimator of u'. For k >= 2, we provide an unbiased estimator of u' that is a modification of the timeaverage estimator and runs with an expected number of time-steps of order k, with O(1=k) expected excess risk. The constant behind the O notation depends on parameters of the regression and is a polylogarithmic function of the smallest eigen...
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作者：Hu, Xiaomeng; Klep, Igor; Nie, Tiawang
作者单位：University of California System; University of California San Diego; University of Ljubljana; University of Primorska
摘要：This paper studies Positivstellensatze and moment problems for sets K that are given by universal quantifiers. Let Q be the closed set of universal quantifiers. Fix a finite nonnegative Borel measure whose support is Q and assume it satisfies the multivariate Carleman condition. First, we prove a Positivstellensatz with universal quantifiers: if a polynomialf is positive on K, then f belongs to the associated quadratic module, under the archimedeanness assumption. Second, we prove some necessa...
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作者：Liu, Peng
作者单位：University of Essex
摘要：In this paper, we study the risk-sharing problem among multiple agents using lambda value at risk (AVaR) as their preferences via the tool of inf-convolution, where AVaR is an extension of value at risk (VaR). We obtain explicit formulas of the infconvolution of multiple AVaR with monotone A and explicit forms of the corresponding optimal allocations, extending the results of the inf-convolution of VaR. It turns out that the inf-convolution of several AVaR is still a AVaR under some mild condi...
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作者：Zhang, Brian Hu; Farina, Gabriele; Celli, Andrea; Sandholm, Tuomas
作者单位：Carnegie Mellon University; Massachusetts Institute of Technology (MIT); Bocconi University
摘要：We study the problem of finding optimal correlated equilibria of various sorts in extensive-form games: normal-form coarse correlated equilibrium (NFCCE), extensive-form coarse correlated equilibrium (EFCCE), and extensive-form correlated equilibrium (EFCE). We make two primary contributions. First, we introduce a new algorithm for computing optimal equilibria in all three notions. Its runtime depends exponentially only on a parameter related to the information structure of the game. We also p...
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作者：Fu, Guanxing; Hager, Paul P.; Horst, Ulrich
作者单位：Hong Kong Polytechnic University; Hong Kong Polytechnic University; University of Vienna; Humboldt University of Berlin; Humboldt University of Berlin
摘要：We consider both N-player and mean-field games of optimal portfolio liquidation in which the players are not allowed to change the direction of trading. Players with an initial short position of stocks are only allowed to buy, while players with an initial long position are only allowed to sell the stock. Under suitable conditions on the model parameters, we show that the games are equivalent to games of timing where the players need to determine the optimal times of market entry and exit. We ...
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作者：Djete, Mao Fabrice
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris
摘要：In order to deal with the question of the existence of a calibrated local stochastic volatility model in finance, we investigate a class of McKean-Vlasov equations where minimal continuity assumption is imposed on the coefficients. Namely, the drift coefficient and, in particular, the volatility coefficient are not necessarily continuous in the measure variable for the Wasserstein topology. In this paper, we provide an existence result and show an approximation by N-particle system or propagat...
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作者：Gurbuzbalabana, Mert
作者单位：Rutgers University New Brunswick; Rutgers University System; Rutgers University New Brunswick
摘要：We consider the problem of minimizing a strongly convex smooth function where the gradients are subject to additive worst-case deterministic errors that are square summable. We study the trade-offs between the convergence rate and robustness to gradient errors when designing the parameters of a first-order algorithm. We focus on a general class of momentum methods (GMM) with constant step size and two momentum parameters that can recover gradient descent (GD), Nesterov's accelerated gradient (...
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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...
