SNELL’S OPTIMIZATION PROBLEM FOR SEQUENCES OF CONVEXCOMPACT VALUED RANDOM SETS

G. Krupa

Abstract: A random set analogue of the Snell problem is presented. In the original Snell’s
problem one observes a sequence of random variables say a gambler’s capital at
successive games. If the gambler leaves the game at a random time his expected
capital at this time is The objective is to stop at time (using information
available up to this moment) such that the expected gambler’s fortune is
maximal.

Here a multivalued analogue of this problem will be studied. Given a Banach space
and a sequence of convex weakly or strongly compact valued random sets
in that space, the existence of a stopping time such that is maximal is
investigated.