機率研討會

主講者: 1.Dr. Eberhard Mayerhofer(Vienna Institute of Finance, Austria) 2.Mr. Tung-Lung Wu (University of Manitoba, Canada)
講題: 1.When are affine processes affine 2.Linear and nonlinear boundary crossing probabilities for Brownian motion and related processes
時間: 2009-06-15 (Mon.)  14:10 - 17:00
地點:
Abstract: (1) A Markov process is affine, if its cumulant generating function is affine in the state-variable. In finite dimensions, it is known that the affine property leads to an analytically tractable class of processes, which allows for numerous applications, for instance in mathematical finance. Only a few years ago, the theory was given mathematical foundations in (Duffie, Filipovic and Schachermayer, 2003), which provides a complete description of affine Markov processes on polyhedral cones. In joint work with Damir Filipovic, we elaborate the maximal range of the affine property, beyond its natural domain. http://www.vif.ac.at/mayerhofer/ (2) In this presentation, we provide a simple general method to obtain the boundary crossing probabilities or the first passage time distribution for linear or nonlinear boundaries for the Brownian motion and related processes.The basic idea of the method is to construct a finite Markov chain through discretization and the waiting for chain entering absorbing state(s) converges to the first passage time of Brownian motion. Numerical examples for various types of boundaries studied in the literature are provided in order to illustrate the method (Joint work with James C. Fu ).
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