Is the FOREX Rate Sequence a Martingale?
The term martingale originally referred to a set of betting strategies popular in France by the 18th Century. These strategies, though appealing at first, could lead to bankruptcy if actually followed. The simplest of these strategies is the one in which the gambler doubles his bet after every loss, so that the first win would recover all previous losses plus win a profit equal to the original stake. Sounds great, but the exponential growth of the bets would eventually bankrupt anyone who chooses to gamble by this Martingale. The modern concept of martingale in probability theory was introduced early in the 20th century by Paul Pierre Lvy, and much of the original development of the theory was done by Joseph Leo Doob among others. The motivation for that work was to show the impossibility of successful betting strategies. This modern concept of martingale applies, not to strategies, but to Stochastic Processes. In other words, these Stochastic Processes are sequences of a random variab
