A prophet inequality for independent random variables with finite variances

1997/12/01 by D. P. Kennedy, Douglas P. Kennedy, Robert P. Kertz +1
Decision Sciences · Mathematics · #Probability and Risk Models #Stochastic processes and statistical mechanics #Random Matrices and Applications

paper · doi:10.2307/3215009

Abstract

It is demonstrated that for each n ≧ 2 there exists a minimal universal constant, c n , such that, for any sequence of independent random variables X r , r ≧ 1 with finite variances, , where the supremum is over all stopping times Τ, 1 ≦ Τ ≦ n. Furthermore, c n ≦ 1/2 and lim inf n → ∞ c n ≧ 0.439485 · ··.

Citations

• Additive comparisons of stop rule and supremum expectations of uniformly bounded independent random variables

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