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Quantitative Finance

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  • $\begingroup$ Exactly, there is no relation between Markov process and Martingale. By definition, a Markov process is a stochastic process that next state has no dependencies on previous state. While a martingale is a process that the drift zero, which does not require the dependencies between different states. see physicsforums.com/showthread.php?t=477725 $\endgroup$ Commented Nov 14, 2013 at 13:27
  • $\begingroup$ The way I think about it a Markov process has a discrete and finite memory, and a martingale has no memory. Hence the conditional expectation of the future is the the same as the current state. A unbiassed brownian motion ($W_t$) or Wiener process is a martingale but a geometric brownian motion with nonzero drift $\mu$ (SDE: $dS_t=\mu S_t dt + \sigma S_t dW_t$) is not. $\endgroup$ Commented Nov 14, 2013 at 15:47
  • $\begingroup$ "Many papers say that stock prices are best modeled using a geometric Brownian motion (GBM)" Actually I doubt many papers say this, as stock prices aren't best modeled with GBM. $\endgroup$ Commented Nov 25, 2013 at 6:49