JSM 2005 Online Program

Abstract #303290

This is the preliminary program for the 2005 Joint Statistical Meetings in Minneapolis, Minnesota. Currently included in this program is the "technical" program, schedule of invited, topic contributed, regular contributed and poster sessions; Continuing Education courses (August 7-10, 2005); and Committee and Business Meetings. This on-line program will be updated frequently to reflect the most current revisions.

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Activity Number:	101
Type:	Contributed
Date/Time:	Monday, August 8, 2005 : 8:30 AM to 10:20 AM
Sponsor:	Business and Economics Statistics Section
Abstract - #303290
Title:	Numerical Approximations for Singular Stochastic Control Problems
Author(s):	Kevin Ross*+
Companies:	University of North Carolina, Chapel Hill
Address:	219 McCauley St, Chapel Hill, NC, 27516, United States
Keywords:	singular stochastic control ; numerical methods ; weak convergence methods ; optimal portfolio selection
Abstract:	We present a general method for obtaining convergent numerical approximations for value functions of singular stochastic control problems. The state process is a stochastic dynamical system constrained to lie in a polyhedral domain; its evolution can be modulated by exercising a control in order to optimize a suitable cost criterion. By singular control, the control process need not be absolutely continuous, thus allowing for large instantaneous changes in the system. The dynamic programming equations for such problems are difficult to work with; in particular, convergence results are not readily available. Our approach to the approximation problem, which follows the Markov chain method, is different in that all our convergence proofs are probabilistic. We apply the method to a problem of optimal portfolio selection under transaction costs.

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