Citation:
David Assaf, Larry Goldstein, and Ester Samuel-Cahn. “Ratio Prophet Inequalities When The Mortal Has Several Choices”. Discussion Papers 2001. Web.
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