-
作者：Andrieu, Christophe; Vihola, Matti
作者单位：University of Bristol; University of Jyvaskyla
摘要：Exact approximations of Markov chain Monte Carlo (MCMC) algorithms are a general emerging class of sampling algorithms. One of the main ideas behind exact approximations consists of replacing intractable quantities required to run standard MCMC algorithms, such as the target probability density in a Metropolis Hastings algorithm, with estimators. Perhaps surprisingly, such approximations lead to powerful algorithms which are exact in the sense that they are guaranteed to have correct limiting ...
-
作者：Diehl, Joscha; Friz, Peter; Mai, Hilmar
作者单位：Technical University of Berlin; University of California System; University of California San Diego; Institut Polytechnique de Paris; ENSAE Paris
摘要：We consider the classical estimation problem of an unknown drift parameter within classes of nondegenerate diffusion processes. Using rough path theory (in the sense of T. Lyons), we analyze the Maximum Likelihood Estimator (MLE) with regard to its pathwise stability properties as well as robustness toward misspecification in volatility and even the very nature of the noise. Two numerical examples demonstrate the practical relevance of our results.
-
作者：Marinucci, Domenico; Vadlamani, Sreekar
作者单位：University of Rome Tor Vergata; Tata Institute of Fundamental Research (TIFR); TIFR Centre for Applicable Mathematics (CAM), Bengaluru
摘要：In this paper, we shall be concerned with geometric functionals and excursion probabilities for some nonlinear transforms evaluated on Fourier components of spherical random fields. In particular, we consider both random spherical harmonics and their smoothed averages, which can be viewed as random wavelet coefficients in the continuous case. For such fields, we consider smoothed polynomial transforms; we focus on the geometry of their excursion sets, and we study their asymptotic behaviour, i...
-
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...
-
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...
-
作者：Corwin, Ivan; Liu, Zhipeng; Wang, Dong
作者单位：Columbia University; Sorbonne Universite; Massachusetts Institute of Technology (MIT); New York University; National University of Singapore
摘要：We prove Airy process variational formulas for the one-point probability distribution of (discrete time parallel update) TASEP with general initial data, as well as last passage percolation from a general down-right lattice path to a point. We also consider variants of last passage percolation with inhomogeneous parameter geometric weights and provide variational formulas of a similar nature. This proves one aspect of the conjectural description of the renormalization fixed point of the Kardar...
-
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 ...
-
作者：Hug, Daniel; Last, Guenter; Schulte, Matthias
作者单位：Helmholtz Association; Karlsruhe Institute of Technology
摘要：Let Z be a Boolean model based on a stationary Poisson process it of compact, convex particles in Euclidean space R-d. Let W denote a compact, convex observation window. For a large class of functionals psi, formulas for mean values of psi(Z boolean AND W) are available in the literature. The first aim of the present work is to study the asymptotic covariances of general geometric (additive, translation invariant and locally bounded) functionals of Z boolean AND W for increasing observation wi...
-
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...
-
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...
