ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

12. Probability and Statistics

1991 MS Classification: 60, 62, 49 Arkin, Vadim I., Central Economics and Mathematics Institute, Russia Optimal stopping problems with restrictions It is considered an optimal stopping problem (relatively the given flow of sigma-algebras) with terminal decision both in discrete and continuous time. Stopping time and terminal decision are subjected to integral restrictions of the equality and inequality type which are given as expectations of some measurable functions. Such problems are occured in sequential analysis and financial mathematics. In the paper we prove neccesary and sufficient optimality conditions (in the form of maximum principle). They give, in particularly, an answer to known A. Wald’s problem: when optimal stopping problem with restrictions is equivalent to Bayesian one.