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Sequential Analysis
Design Methods and Applications
Volume 27, 2008 - Issue 4
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Original Articles

On Wald Optimal Stopping Problem for Geometric Brownian Motions

Pages 435-440 | Received 01 Oct 2007, Accepted 05 Jul 2008, Published online: 31 Oct 2008

REFERENCES

  • Bensoussan , A. ( 1975 ). Variational Inequalities and Optimal Stopping Time Problems, Proceedings of a Symposium, Mathematics Research Center, University of Wisconsin–Madison , pp. 219 – 244 .
  • Burkholder , D. L. ( 1966 ). Martingale Transforms, Annals of Mathematical Statistics 37 : 1494 – 1504 .
  • Burkholder , D. L. ( 1973 ). Distribution Function Inequalities for Martingales, Annals of Probability 1 : 19 – 42 .
  • Friedman , A. ( 1975 ). Stochastic Differential Equations and Applications , vol. 1 , New York : Academic Press .
  • Graversen , S. E. and Peskir , G. ( 1997 ). On Wald-Type Optimal Stopping for Brownian Motion, Journal of Applied Probability 34 : 66 – 73 .
  • Graversen , S. E. and Peskir , G. ( 1998 ). Optimal Stopping and Maximal Inequalities for Geometric Brownian Motion, Journal of Applied Probability 35 : 856 – 872 .
  • Hu , Y. and Øksendal , B. ( 1998 ). On Optimal Time to Invest When Price Processes are Geometric Brownian Motions, Finance and Stochastics 2 : 295 – 310 .
  • Lai , T. L. ( 2004 ). Likelihood Ratio Identities and Their Applications to Sequential Analysis (with discussions), Sequential Analysis 23 : 467 – 556 .
  • McDonald , R. and Siegel , D. ( 1986 ). The Value of Waiting to Invest, Quarterly Journal of Economics 101 : 707 – 727 .
  • Olsen , T. E. and Stensland , G. ( 1992 ). On Optimal Timing of Investment When Cost Components are Additive and Follow Geometric Diffusions, Journal of Economics and Dynamics Control 16 : 39 – 51 .
  • Robbins , H. and Samuel , E. ( 1966 ). An Extension of a Lemma of Wald, Journal of Applied Probability 3 : 272 – 273 .
  • Salminen , P. ( 1985 ). Optimal Stopping of One-Dimensional Diffusions, Mathematische Nachrichten 124 : 85 – 101 .
  • Shepp , L. A. and Shiryaev , A. N. ( 1993 ). The Russian Option: Reduced Regret, Annals of Applied Probability 3 : 631 – 640 .
  • Shiryaev , A. ( 1978 ). Optimal Stopping Rules , Springer : Berlin .
  • Van Moerbeke , P. ( 1976 ). On Optimal Stopping and Free Boundary Problems, Archive for Rational Mechanics and Analysis 60 : 101 – 148 .
  • Wald , A. ( 1945 ). Sequential Test of Statistical Hypotheses, Annals of Mathematical Statistics 16 : 117 – 186 .
  • Wald , A. ( 1946 ). Differentiation Under the Expectation Sign in the Fundamental Identity of Sequential Analysis, Annals of Mathematical Statistics 17 : 493 – 497 .
  • Recommended by Nitis Mukhopadhyay

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