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作者：Peled, Ron
作者单位：New York University
摘要：Intuitively, two metric spaces are rough isometric (or quasi-isometric) if their large-scale metric structure is the same, ignoring fine details. This concept has proven fundamental in the geometric study of groups. Abert, and later Szegedy and Benjamini, have posed several probabilistic questions concerning this concept. In this article, we consider one of the simplest of these: are two independent Poisson point processes on the line rough isometric almost surely? Szegedy conjectured that the...
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作者：Kallsen, J.; Muhle-Karbe, J.
作者单位：University of Kiel; University of Vienna
摘要：We consider the problem of maximizing expected utility from terminal wealth in models with stochastic factors. Using martingale methods and a conditioning argument, we determine the optimal strategy for power utility under the assumption that the increments of the asset price are independent conditionally on the factor process.
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作者：de Saporta, Benoite; Dufour, Francois; Gonzalez, Karen
作者单位：Universite de Bordeaux
摘要：We propose a numerical method to approximate the value function for the optimal stopping problem of a piecewise deterministic Markov process (PDMP). Our approach is based on quantization of the post jump location-inter-arrival time Markov chain naturally embedded in the PDMP, and path-adapted time discretization grids. It allows us to derive bounds for the convergence rate of the algorithm and to provide a computable epsilon-optimal stopping time. The paper is illustrated by a numerical example.
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作者：Sezer, Semih Onur
作者单位：Sabanci University
摘要：In the Wiener disorder problem, the drift of a Wiener process changes suddenly at some unknown and unobservable disorder time. The objective is to detect this change as quickly as possible after it happens. Earlier work on the Bayesian formulation of this problem brings optimal (or asymptotically optimal) detection rules assuming that the prior distribution of the change time is given at time zero, and additional information is received by observing the Wiener process only. Here, we consider a...
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作者：Kella, Offer; Yor, Marc
作者单位：Hebrew University of Jerusalem; Sorbonne Universite; Universite Paris Cite
摘要：We give a representation of the solution for a stochastic linear equation of the form X-t = Y-t + integral((0,t]) X-s-dZ(s) where Z is a cadlag semimartingale and Y is a cadlag adapted process with bounded variation on finite intervals. As an application we study the case where Y and -Z are nondecreasing, jointly have stationary increments and the jumps of -Z are bounded by 1. Special cases of this process are shot-noise processes, growth collapse (additive increase, multiplicative decrease) p...
