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 = Xt ∫0t Xs d s - t is also a martingale.
All Science Journal Classification (ASJC) codes
- Management Science and Operations Research
- Industrial and Manufacturing Engineering
- Applied Mathematics
- dollar cost averaging
- system theorems