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作者：Beiglboeck, Mathias; Jourdain, Benjamin; Margheriti, William; Pammer, Gudmund
作者单位：University of Vienna; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：While many questions in (robust) finance can be posed in the martingale optimal transport (MOT) framework, others require to consider also nonlinear cost functionals. Following the terminology of Gozlan, Roberto, Samson and Tetali (J. Funct. Anal. 273 (2017) 3327-3405) for classical optimal transport, this corresponds to weak martingale optimal transport (WMOT).In this article we establish stability of WMOT which is important since financial data can give only imprecise information on the unde...
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作者：Doukhan, Paul; Neumann, Michael h.; Truquet, Lionel
作者单位：CY Cergy Paris Universite; Friedrich Schiller University of Jena
摘要：The first motivation of this paper is to study stationarity and ergodic properties for a general class of time series models defined conditional on an exogenous covariates process. The dynamic of these models is given by an autoregressive latent process which forms a Markov chain in random environments. Contrarily to existing contributions in the field of Markov chains in random environments, the state space is not discrete and we do not use small set type assumptions or uniform contraction co...
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作者：Djehiche, Boualem; Elie, Romuald; Hamadene, Said
作者单位：Royal Institute of Technology; Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Le Mans Universite
摘要：In this paper, we study a class of reflected backward stochastic differen-tial equations (BSDEs) of mean-field type, where the mean-field interaction in terms of the distribution of the Y-component of the solution enters in both the driver and the lower obstacle. We consider in details the case where the lower obstacle is a deterministic function of (Y, E[Y]) and discuss the more general dependence on the distribution of Y. Under mild Lipschitz and in-tegrability conditions on the coefficients...
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作者：Benaych-Georges, Florent; Bouchaud, Jean-Philippe; Potters, Marc
摘要：We give a new algorithm for the estimation of the cross-covariance ma-trix EXY' of two large-dimensional signals X e Rn, Y e Rp in the context where the number T of observations of the pair (X, Y) is large but n/T and p/ T are not supposed to be small. In the asymptotic regime where n, p, T are large, with high probability, this algorithm is optimal for the Frobenius norm among rotationally invariant estimators, that is, estimators derived from the empirical estimator by cleaning the singular ...
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作者：Hernandez, Camilo; Possamai, Dylan
作者单位：Imperial College London; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We develop a theory for continuous-time non-Markovian stochastic con-trol problems which are inherently time-inconsistent. Their distinguishing feature is that the classical Bellman optimality principle no longer holds. Our formulation is cast within the framework of a controlled non-Markovian for-ward stochastic differential equation, and a general objective functional set-ting. We adopt a game-theoretic approach to study such problems, meaning that we seek for subgame perfect Nash equilibriu...
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作者：Feng, Renjie; Tian, Gang; Wei, Dongyi
作者单位：Max Planck Society; Peking University
摘要：We will prove the Berry-Esseen theorem for the number counting function of the circular beta-ensemble (C beta E), which will imply the central limit theorem for the number of points in arcs of the unit circle in mesoscopic and macroscopic scales. We will prove the main result by estimating the characteristic functions of the Prufer phases and the number counting function, which will imply the uniform upper and lower bounds of their variance. We also show that the similar results hold for the S...
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作者：Chernozhukov, Victor; Chetverikov, Denis; Koike, Yuta
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); University of California System; University of California Los Angeles; University of Tokyo; University of Tokyo
摘要：In this paper, we derive new, nearly optimal bounds for the Gaussian ap-proximation to scaled averages of n independent high-dimensional centered random vectors X1, . .. , Xn over the class of rectangles in the case when the covariance matrix of the scaled average is nondegenerate. In the case of bounded Xi's, the implied bound for the Kolmogorov distance between the distribution of the scaled average and the Gaussian vector takes the form C(Bn2 log3 d/n)1/2log n, where d is the dimension of t...
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作者：Breden, Maxime; Engel, Maximilian
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Free University of Berlin
摘要：We confirm a long-standing conjecture concerning shear-induced chaos in stochastically perturbed systems exhibiting a Hopf bifurcation. The method of showing the main chaotic property, a positive Lyapunov exponent, is a computer-assisted proof. Using the recently developed theory of conditioned Lyapunov exponents on bounded domains and the modified Furstenberg- Khasminskii formula, the problem boils down to the rigorous computation of eigenfunctions of the Kolmogorov operators describing distr...
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作者：Grama, Ion; Liu, Quansheng; Pin, Erwan
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Consider a multitype branching process in a random environment, whose reproduction law of generation n depends on the random environment at time n, unlike a constant distribution assumed in the Galton-Watson process. The famous Kesten-Stigum theorem for a supercritical multitype Galton-Watson process gives a precise description of the exponential increasing rate of the population size via a criterion for the nondegeneracy of the fundamental mar-tingale. Finding the corresponding result in the ...
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作者：Lacker, Daniel; Ramanan, Kavita; Wu, Ruoyu
作者单位：Columbia University; Brown University; Iowa State University
摘要：We study the limiting behavior of interacting particle systems indexed by large sparse graphs, which evolve either according to a discrete time Markov chain or a diffusion, in which particles interact directly only with their nearest neighbors in the graph. To encode sparsity we work in the framework of local weak convergence of marked (random) graphs. We show that the joint law of the particle system varies continuously with respect to local weak conver-gence of the underlying graph marked wi...
