Simulation approach to optimal stopping in some blackjack type problems

• Autorzy: Grzybowski A. Z.
• Języki publikacji: EN

Abstrakty

EN

In the paper, an unbounded blackjack type optimal stopping problem is considered. A decision maker (DM) observes sequentially the values of an infinite sequence of nonnegative random variables. After each observation, the DM decides whether to stop or to continue. If the DM decides to stop at a given moment, the obtains a payoff dependent on the sum of already observed values. The greater the sum, the more the DM gains, unless the sum exceeds a given positive number. If so, the decision maker loses all or part of the payoff. It turns out that under some elementary assumptions the optimal stopping rule (OSR) for such a problem has a very simple, so-called threshold form. However, even in very simple cases, the value of the problem has no closed analytical form. Therefore, it is very hard to evaluate the value directly. Thus, in order to find the relationship between the problem design parameters and the value of the problem, is proposed studying the relation via Monte Carlo simulations combined with regression analysis The same approach is adopted to examine the OSR risk characteristics.

Słowa kluczowe

EN

optimal stopping; Monte Carlo simulation; regression analysis; blackjack type problem

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
• Rocznik: 2011
• Tom: Vol. 10, nr 2
• Strony: 75--86
• Opis fizyczny: Bibliogr. 19 poz., rys.

Twórcy

autor

Grzybowski A. Z.

• Institute of Mathematics, Czestochowa University of Technology, Poland,

Bibliografia

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