A prophet inequality for independent random variables with finite variances
Douglas P. Kennedy, Robert P. Kertz · Journal of Applied Probability · 1997
It is demonstrated that for each n ≧ 2 there exists a minimal universal constant, cn, such that, for any sequence of independent random variables {Xr, r ≧ 1} with finite variances, , where the supremum is over all stopping times Τ, 1 ≦ Τ ≦ n. Furthermore, cn ≦ 1/2 and lim inf n→ ∞ cn ≧ 0.439485 · ··.