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作者：Cerny, Ales; Kallsen, Jan
作者单位：City St Georges, University of London; Technical University of Munich; Aalto University
摘要：We provide a new characterization of mean-variance hedging strategies in a general semimartingale market. The key point is the introduction of a new probability measure P* which turns the dynamic asset allocation problem into a myopic one. The minimal martingale measure relative to P* coincides with the variance-optimal martingale measure relative to the original probability measure P.
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作者：Comets, Francis; Popov, Serguei
作者单位：Universite Paris Cite; Universidade de Sao Paulo
摘要：We study branching random walks in random i.i.d. environment in Z(d), d >= 1. For this model, the population size cannot decrease, and a natural definition of recurrence is introduced. We prove a dichotomy for recurrence/transience, depending only on the support of the environmental law. We give sufficient conditions for recurrence and for transience. In the recurrent case, we study the asymptotics of the tail of the distribution of the hitting times and prove a shape theorem for the set of la...
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作者：Dong, Hongjie; Krylov, N. V.
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Time-inhomogeneous controlled diffusion processes in both cylindrical and noncylindrical domains are considered. Bellman's principle and its applications to proving the continuity of value functions are investigated.
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作者：Bertoin, Jean
作者单位：Sorbonne Universite; Universite Paris Cite; Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider a Langevin process with white noise random forcing. We suppose that the energy of the particle is instantaneously absorbed when it hits some fixed obstacle. We show that nonetheless, the particle can be instantaneously reflected, and study some properties of this reflecting solution.
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作者：Kendall, Wilfrid S.
作者单位：University of Warwick
摘要：It is shown how to construct a successful co-adapted coupling of two copies of an n-dimensional Brownian motion (B-1,..., B-n) while simultaneously coupling all corresponding copies of Levy stochastic areas integral B-i d B-j - integral B-j dB(i). It is conjectured that successful co-adapted couplings still exist when the Levy stochastic areas are replaced by a finite set of multiply iterated path- and time-integrals, subject to algebraic compatibility of the initial conditions.
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作者：Kaj, Ingemar; Leskela, Lasse; Norros, Ilkka; Schmidt, Volker
作者单位：Uppsala University; Aalto University; Ulm University
摘要：This paper studies the limits of a spatial random field generated by uniformly scattered random sets, as the density lambda of the sets grows to infinity and the mean volume rho of the sets tends to zero. Assuming that the volume distribution has a regularly varying tail with infinite variance, we show that the centered and renormalized random field can have three different limits, depending on the relative speed at which lambda and rho are scaled. If lambda grows much faster than rho shrinks,...
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作者：Barany, Imre; Vu, Van
作者单位：Hungarian Academy of Sciences; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; University of London; University College London; Rutgers University System; Rutgers University New Brunswick
摘要：Choose n random, independent points in R-d according to the standard normal distribution. Their convex hull K-n is the Gaussian random polytope. We prove that the volume and the number of faces of K-n satisfy the central limit theorem, settling a well-known conjecture in the field.
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作者：Aldous, David
作者单位：University of California System; University of California Berkeley
摘要：Consider routing traffic on the N x N torus, simultaneously between all source-destination pairs, to minimize the cost Sigma e c(e)f(2) (e), where f (e) is the volume of flow across edge e and the c(e) form an i.i.d. random environment. We prove existence of a rescaled N -> infinity limit constant for minimum cost, by comparison with an appropriate analogous problem about minimum-cost flows across a M x M subsquare of the lattice.
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作者：Guionnet, Alice; Maurel-Segala, Edouard
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：We study several-matrix models and show that when the potential is convex and a small perturbation of the Gaussian potential, the first order correction to the free energy can be expressed as a generating function for the enumeration of maps of genus one. In order to do that, we prove a central limit theorem for traces of words of the weakly interacting random matrices defined by these matrix models and show that the variance is a generating function for the number of planar maps with two vert...
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作者：Debussche, Arnaud; Zambotti, Lorenzo
作者单位：Universite Paris Cite; Sorbonne Universite
摘要：We consider a stochastic partial differential equation with reflection at 0 and with the constraint of conservation of the space average. The equation is driven by the derivative in space of a space-time white noise and contains a double Laplacian in the drift. Due to the lack of the maximum principle for the double Laplacian, the standard techniques based on the penalization method do not yield existence of a solution. We propose a method based on infinite dimensional integration by parts for...
