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作者：Coghi, Michele; Flandoli, Franco
作者单位：Scuola Normale Superiore di Pisa; University of Pisa
摘要：A system of interacting particles described by stochastic differential equations is considered. As oppopsed to the usual model, where the noise perturbations acting on different particles are independent, here the particles are subject to the same space-dependent noise, similar to the (noninteracting) particles of the theory of diffusion of passive scalars. We prove a result of propagation of chaos and show that the limit PDE is stochastic and of inviscid type, as opposed to the case when inde...
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作者：Fathi, Max; Maas, Jan
作者单位：Sorbonne Universite; Institute of Science & Technology - Austria
摘要：We develop a new and systematic method for proving entropic Ricci curvature lower bounds for Markov chains on discrete sets. Using different methods, such bounds have recently been obtained in several examples (e.g., 1-dimensional birth and death chains, product chains, Bernoulli-Laplace models, and random transposition models). However, a general method to obtain discrete Ricci bounds had been lacking. Our method covers all of the examples above. In addition, we obtain new Ricci curvature bou...
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作者：Hoffman, Christopher; Johnson, Tobias; Junge, Matthew
作者单位：University of Washington; University of Washington Seattle; University of Southern California
摘要：Consider the following interacting particle system on the d-ary tree, known as the frog model: Initially, one particle is awake at the root and i.i.d. Poisson many particles are sleeping at every other vertex. Particles that are awake perform simple random walks, awakening any sleeping particles they encounter. We prove that there is a phase transition between transience and recurrence as the initial density of particles increases, and we give the order of the transition up to a logarithmic fa...
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作者：Najim, Jamal; Yao, Jianfeng
作者单位：Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Information Sciences & Technologies (INS2I); ESIEE Paris; Institut Polytechnique de Paris; Ecole des Ponts ParisTech; Centre National de la Recherche Scientifique (CNRS); IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris
摘要：Consider a N x n matrix Sigma(n) = 1 root n R-n(1/2) X-n, where R-n is a nonnegative definite Hermitian matrix and X-n is a random matrix with i.i.d. real or complex standardized entries. The fluctuations of the linear statistics of the eigenvalues Trace f (Sigma(n) Sigma(n)*) = Sigma(N)(i=1) f (lambda(i)), (lambda(i)) eigenvalues of Sigma(n) Sigma(n)*, are shown to be Gaussian, in the regime where both dimensions of matrix Sigma(n) go to infinity at the same pace and in the case where f is of...
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作者：Bornemann, Folkmar
作者单位：Technical University of Munich
摘要：In a recent paper, Edelman, Guionnet and Peche conjectured a particular n(-1) correction term of the smallest eigenvalue distribution of the Laguerre unitary ensemble (LUE) of order n in the hard-edge scaling limit: specifically, the derivative of the limit distribution, that is, the density, shows up in that correction term. We give a short proof by modifying the hard-edge scaling to achieve an optimal O(n(-2)) rate of convergence of the smallest eigenvalue distribution. The appearance of the...
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作者：Karatzas, Ioannis; Sarantsev, Andrey
作者单位：Columbia University; University of Washington; University of Washington Seattle
摘要：We study models of regulatory breakup, in the spirit of Strong and Fouque [Ann. Finance 7 (2011) 349-374] but with a fluctuating number of companies. An important class of market models is based on systems of competing Brownian particles: each company has a capitalization whose logarithm behaves as a Brownian motion with drift and diffusion coefficients depending on its current rank. We study such models with a fluctuating number of companies: If at some moment the share of the total market ca...
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作者：Bapst, Victor; Coja-Oghlan, Amin; Rassmann, Felicia
作者单位：Goethe University Frankfurt
摘要：Diluted mean-field models are graphical models in which the geometry of interactions is determined by a sparse random graph or hypergraph. Based on a nonrigorous but analytic approach called the cavity method, physicists have predicted that in many diluted mean-field models a phase transition occurs as the inverse temperature grows from 0 to infinity [Proc. National Academy of Sciences 104 (2007) 10318-10323]. In this paper, we establish the existence and asymptotic location of this so-called ...
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作者：Bank, Peter; Dolinsky, Yan; Goekay, Selim
作者单位：Technical University of Berlin; Hebrew University of Jerusalem
摘要：We study super-replication of contingent claims in an illiquid market with model uncertainty. Illiquidity is captured by nonlinear transaction costs in discrete time and model uncertainty arises as our only assumption on stock price returns is that they are in a range specified by fixed volatility bounds. We provide a dual characterization of super-replication prices as a supremum of penalized expectations for the contingent claim's payoff. We also describe the scaling limit of this dual repre...
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作者：Czichowsky, Christoph; Schachermayer, Walter
作者单位：University of London; London School Economics & Political Science; University of Vienna
摘要：We consider the problem of portfolio optimisation with general cadlag price processes in the presence of proportional transaction costs. In this context, we develop a general duality theory. In particular, we prove the existence of a dual optimiser as well as a shadow price process in an appropriate generalised sense. This shadow price is defined by means of a sandwiched process consisting of a predictable and an optional strong supermartingale, and pertains to all strategies that remain solve...
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作者：Embrechts, Paul; Hofert, Marius; Wang, Ruodu
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Swiss Finance Institute (SFI); Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Waterloo
摘要：The tail-dependence compatibility problem is introduced. It raises the question whether a given d x d-matrix of entries in the unit interval is the matrix of pairwise tail-dependence coefficients of a d-dimensional random vector. The problem is studied together with Bernoulli-compatible matrices, that is, matrices which are expectations of outer products of random vectors with Bernoulli margins. We show that a square matrix with diagonal entries being 1 is a tail-dependence matrix if and only ...
