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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 83, 2011 - Issue 4-6: Optimal stopping with Applications
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Original Articles

A harmonic function technique for the optimal stopping of diffusions

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Pages 347-363 | Received 29 Oct 2009, Accepted 02 Jun 2010, Published online: 09 Jun 2011

References

  • Beibel , M. and Lerche , H.R. 1997 . A new look at optimal stopping problems related to mathematical finance . Stat. Sin. , 7 ( 1 ) : 93 – 108 .
  • Beibel , M. and Lerche , H.R. 2000 . A note on optimal stopping of regular diffusions under random discounting . Teor. Veroyatnost. i Primenen. , 45 ( 4 ) : 657 – 669 .
  • Borodin , A.N. and Salminen , P. 2002 . “ Handbook of Brownian motion – facts and formulae ” . In Probability and its Applications , Basel : Birkhäuser Verlag . pp. xvi+672
  • Dayanik , S. and Karatzas , I. 2003 . On the optimal stopping problem for one-dimensional diffusions . Stoch. Process. Appl. , 107 ( 2 ) : 173 – 212 .
  • Helmes , K. and Stockbridge , R.H. 2010 . Construction of the value function and optimal rules in optimal stopping of one-dimensional diffusions . Adv. Appl. Probab. , 42 ( 1 ) : 158 – 182 .
  • Hu , Y. and Øksendal , B. 1998 . Optimal time to invest when the price processes are geometric Brownian motions . Finance Stoch. , 2 ( 3 ) : 295 – 310 .
  • Itô , K. and McKean , H.P. Jr . 1974 . “ Diffusion processes and their sample paths ” . In Die Grundlehren der Mathematischen Wissenschaften, Band 125 , Berlin : Springer-Verlag . pp. xv+321
  • Lerche , H.R. and Urusov , M. 2007 . Optimal stopping via measure transformation: The Beibel-Lerche approach . Stochastics , 79 ( 3–4 ) : 275 – 291 .
  • McDonald , R. and Siegel , D. 1986 . The value of waiting to invest . Q. J. Econ. , 101 ( 4 ) : 707 – 727 .
  • Mucci , A.G. 1978/79 . Existence and explicit determination of optimal stopping times . Stoch. Process. Appl. , 8 ( 1 ) : 33 – 58 .
  • Olsen , T. and Stensland , G. 1992 . On optimal timing of investment when cost components are additive and follows geometric diffusions . J. Econ. Dyn. Control , 16 : 39 – 51 .
  • Pinsky , R.G. 1995 . “ Positive harmonic functions and diffusion ” . In Cambridge Studies in Advanced Mathematics , Cambridge : Cambridge University Press . pp. xvi+474
  • Salminen , P. 1985 . Optimal stopping of one-dimensional diffusions . Math. Nachr. , 124 : 85 – 101 .
  • Taylor , H.M. 1968 . Optimal stopping in a Markov process . Ann. Math. Stat. , 39 : 1333 – 1344 .
  • Wong , S.K.T. 2008 . The generalized perpetual American exchange-option problem . Adv. Appl. Probab. , 40 ( 1 ) : 163 – 182 .

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