Publication Cover
Stochastics
An International Journal of Probability and Stochastic Processes
Volume 83, 2011 - Issue 4-6: Optimal stopping with Applications
142
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Constructing time-homogeneous generalized diffusions consistent with optimal stopping values

&
Pages 477-503 | Received 04 Nov 2009, Accepted 06 Sep 2010, Published online: 09 Jun 2011

References

  • Alfonsi , A. and Jourdain , B. 2008 . General duality for perpetual American options . Int. J. Theoret. Appl. Finance , 11 ( 6 ) : 545 – 566 .
  • Alfonsi , A. and Jourdain , B. 2009 . Exact volatility calibration based on a dupire-type call-put duality for perpetual American options . Nonlinear Differ. Equ. Appl. , 16 ( 4 ) : 523 – 554 .
  • Borodin , A.N. and Salminen , P. 2002 . Handbook of Brownian Motion – Facts and Formulae , 2nd ed. , Basel : Birkhäuser .
  • Carlier , G. 2003 . Duality and existence for a class of mass transportation problems and economic applications . Adv. Math. Econ. , 5 : 1 – 22 .
  • Dym , H. and McKean , H.P. 1976 . Gaussian Processes, Function Theory, and the Inverse Spectral Problem , New York : Academic Press, Inc. .
  • E. Ekström and D. Hobson, Recovering a time-homogeneous stock price process from perpetual option prices, to appear in Ann. Appl. Probab. Available at http://arxiv.org/abs/0903.4833
  • Feller , W. 1959 . The birth and death processes as diffusion processes . J. Math. Pure Appl. , 38 : 301 – 345 .
  • Gangbo , W. and McCann , R.J. 1996 . The geometry of optimal transportation . Acta Math. , 177 ( 2 ) : 113 – 161 .
  • Itô , K. and McKean , H.P. 1974 . Diffusion Processes and their Sample Paths , Berlin : Springer-Verlag .
  • Kac , I.S. 2005 . Pathological birth-and-death processes and the spectral theory of strings . Funct. Anal. Appl. , 39 ( 2 ) : 144 – 147 .
  • Kotani , S. and Watanabe , S. 1982 . “ Krein's spectral theory of strings and generalized diffusion processes ” . In Functional Analysis in Markov Processes , Lecture Notes in Mathematics, 923 Edited by: Fukushima , M. 235 – 259 .
  • Rachev , S.T. and Rüschendorf , L. 1998 . Mass Transportation Problems , Vol. 1 , Berlin/New York : Springer-Verlag .
  • Rockafellar , R.T. 1970 . Convex Analysis , Princeton, NJ : Princeton University Press .
  • Rogers , L.C.G. and Williams , D. 2000 . Diffusions, Markov Processes and Martingales , Vol. 2 , Cambridge : Cambridge University Press .
  • Rüschendorf , L. 1991 . “ Fréchet-bounds and their applications ” . In Advances in Probability Distributions with Given Marginals: Beyond the Copulas , Edited by: Dall′Aglio , G. , Kotz , S. and Salinetti , G. 151 – 187 . Dordrecht : Kluwer Academic Publishers .
  • Rüschendorf , L. 2007 . Monge–Kantorovich transportation problem and optimal couplings . Jahresbericht der DMV , 109 : 113 – 137 .
  • Rüschendorf , L. and Uckelmann , L. 2000 . Numerical and analytical results for the transportation problem of Monge–Kantorovich . Metrika , 51 ( 3 ) : 245 – 258 .
  • Villani , C. 2009 . Optimal Transport: Old and New , Berlin : Springer-Verlag .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.