A martingale system theorem for stock investments

Robert J. Vanderbei

Research output: Contribution to journalArticlepeer-review


In this paper a proof is given that the dollar-cost-averaging investment strategy yields no advantage over any other non-clairvoyant strategy by showing that the difference between any two strategies is a mean-zero martingale. An interesting corollary of this theorem is that if Xt is a continuous positive martingale then the process Yt = Xt0t Xs d s - t is also a martingale.

Original languageEnglish (US)
Pages (from-to)155-159
Number of pages5
JournalOperations Research Letters
Issue number3
StatePublished - May 1990
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Software
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Applied Mathematics


  • dollar cost averaging
  • martingales
  • system theorems


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