Optimal Stopping for Partial Sums

1972/08/01 by D. A. Darling, T. Liggett, Thomas M. Liggett +2 · 3 citations
Computer Science · Decision Sciences · #Optimization and Search Problems #Auction Theory and Applications #Distributed systems and fault tolerance

paper · pdf · doi:10.1214/aoms/1177692491

Abstract

We determine sup E\lbrack r(S_T)\rbrack, where S_n is a sequence of partial sums of independent identically distributed random variables, for two reward functions: r(x) = x⁺ and r(x) = (e^x - 1)⁺. The supremum is taken over all stop rules T. We give conditions under which the optimal expected return is finite. Under these conditions, optimal stopping times exist, and we determine them. The problem has an interpretation in an action timing problem in finance.

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