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Prophet compared to gambler: additive inequalities for transforms of sequences of random variables

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  • Boshuizen, Frans A.

Abstract

Additive comparisons are given between optimal expected gains of a prophet and a gambler. A gambler knows only the past and the present and a prophet is a player with complete foresight. The optimal expected gains are obtained by betting on differences of consecutive uniformly bounded random variables. For example, if the random variables are i.i.d. and [0,1]-valued, then the difference between the prophet and the gambler is at most n/16 for a game of length n, and the bound n/16 is the best possible.

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  • Boshuizen, Frans A., 1996. "Prophet compared to gambler: additive inequalities for transforms of sequences of random variables," Statistics & Probability Letters, Elsevier, vol. 29(1), pages 23-32, August.
    • Handle: RePEc:eee:stapro:v:29:y:1996:i:1:p:23-32
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    References listed on IDEAS

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    1. MERTENS, Jean-François & ZAMIR, Shmuel, 1977. "The maximal variation of a bounded martingale," LIDAM Reprints CORE 309, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Boshuizen, F. A., 1994. "Optimal Stopping-Related Inequalities for Iid Random Variables when the Future Is Discounted," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 115-131, July.
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