Ratio Prophet Inequalities When the Mortal Has Several Choices

Citation:

David Assaf, L. G., & Samuel-Cahn, E. . (2001). Ratio Prophet Inequalities When the Mortal Has Several Choices. Discussion Papers. presented at the 2, Annals of Applied Probability 12 (2002) 972-984. Retrieved from /files/dp236.pdf

Abstract:

Let X_i be non-negative, independent random variables with finite expectation, and X*_n=maxX_1,...,X_n. The value EX*_n is what can be obtained by a "prophet". A "mortal" on the other hand, may use k>=1 stopping rules t_1,...,t_k, yielding a return of E[max_i=1,...,k X_t_i]. For n>=k the optimal return is V^n_k(X_1,...,X_n)=supE[max_i=1,...,k X_t_i] where the supremum is over all stopping rules t_1,...t_k such that P(t_i

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