Wald's martingale

In probability theory Wald's martingale, named after Abraham Wald and more commonly known as the geometric Brownian motion, is a stochastic process of the form

\left\{\exp\left(\lambda W_t-\frac{1}{2}\lambda^2t\right),t\geq 0\right\}

for any real value λ where Wt is a Wiener process.[1]:32[2]:261[3] The process is a martingale.[1]

See also

Notes

  1. 1 2 Hunt, P. J.; Kennedy, J. E. (2005). "Martingales". Financial Derivatives in Theory and Practice. Wiley Series in Probability and Statistics. p. 31. doi:10.1002/0470863617.ch3. ISBN 9780470863619.
  2. ↑ Chang, F. R. (2004). "Boundaries and Absorbing Barriers". Stochastic Optimization in Continuous Time. p. 225. doi:10.1017/CBO9780511616747.008. ISBN 9780511616747.
  3. ↑ Asmussen, S. R.; Kella, O. (2000). "A multi-dimensional martingale for Markov additive processes and its applications". Adv. In Appl. Probab. 32 (2): 376–393. doi:10.1239/aap/1013540169. JSTOR 1428194.
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