[Winter 1999 Colloquiums]
[Department Homepage]

COLLOQUIUM

DEPARTMENT OF MATHEMATICS AND STATISTICS
OAKLAND UNIVERSITY
ROCHESTER, MICHIGAN 48309

John Birge
Department of Industrial and Operations Engineering
University of Michigan

Optimality Conditions for Dynamic Stochastic Programs:
Applications in Finance and Scheduling

Abstract

Dynamic stochastic optimization problems arise in a variety of contexts. We give some general optimality criteria for these problems based first on convexity arguments. We show how these criteria provide insightful characteristics for scheduling and financial problems. The scheduling result is a form of turnpike theorem while the financial result the equivalence of the no-arbitrage condition and the existence of a risk-neutral measure. We extend these results by showing how each can include non-convexities such as setup or fixed transaction costs. We then give a limiting result in which the convex lagrangian dual asymptotically obtains an optimal solution to the non-convex original problem.

372 Science and Engineering Building
Tuesday, February 9, 1999
3:00­4:00 P.M.

Refreshments at 2:30­3:00 PM in Room 368, Science and Engineering Building