Optimal switching among several Brownian motions

Optimal switching among several Brownian motions

0.00 Avg rating0 Votes
Article ID: iaor1993416
Country: United States
Volume: 30
Issue: 5
Start Page Number: 1150
End Page Number: 1162
Publication Date: Sep 1992
Journal: SIAM Journal on Control and Optimization
Authors:
Keywords: markov processes
Abstract:

For equ1let equ2be a one-dimensional Brownian motion on the interval equ3with absorption at the endpoints. At each instant in time, one must decide to run some subset of these d Brownian motions while holding the others fixed at their current state. The resulting process evolves in the rectangle equ4. If, at some instant, one decides to freeze all of the Brownian motions, then a reward is received in accordance with this final position. Two types of reward functions are considered. First, it is assumed that the reward is zero everywhere in D, except along the d edges that correspond to the coordinate axes. Along these edges, it is given by equ5strictly concave functions equ6, which are zero at the endpoints 0 and equ7of their domains. The optimal control for this problem has a simple description. Let equ8and put equ9. It is proved that the optimal control is: On equ10run any Brownian motion except the ith and stop the first time an edge is reached. The second class of reward functions are assumed to be zero everywhere except on the facets of D that meet at the origin. On the equ11such facet (i.e., where equ12), the reward function is the product of equ13for equ14. Put equ15. The optimal control is: On equ16run the equ17Brownian motion and stop when a facet of D is reached.

Reviews

Required fields are marked *. Your email address will not be published.