Snell's optimization problem for sequences of convex compact valued random sets

• Autorzy: Krupa G.
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

Snell problem; random variables; Banach space

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2003
• Tom: Vol. 23, Fasc. 1
• Strony: 77--91
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Krupa G.

• Department of Mathematics and Nature, The Catholic University of Lublin, Al. Racławickie 14, 20-950 Lublin, Poland

Bibliografia

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