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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 23, Fasc. 1,
pages 77 - 91
 

SNELL’S OPTIMIZATION PROBLEM FOR SEQUENCES OF CONVEX COMPACT 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 (q), n say a gambler’s capital at successive games. If the gambler leaves the game at a random time n, his expected capital at this time is Eq . n The objective is to stop at time n (using information available up to this moment) such that the expected gambler’s fortune Eq , n 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 (Z ) n in that space, the existence of a stopping time n such that EZ n is maximal is investigated.

2000 AMS Mathematics Subject Classification: 60G40, 62L15, 28B20, 26E25, 54C60.

Key words and phrases: -

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