Publication Cover
Stochastics
An International Journal of Probability and Stochastic Processes
Volume 79, 2007 - Issue 1-2: Optimal Stopping and Applications Part I
146
Views
30
CrossRef citations to date
0
Altmetric
Original Articles

The duality of optimal exercise and domineering claims: a Doob–Meyer decomposition approach to the Snell envelope

Pages 27-60 | Received 06 Mar 2006, Accepted 04 Oct 2006, Published online: 05 Nov 2008

References

  • Andersen , L. and Broadie , M. 2004 . A primal-dual simulation algorithm for pricing multidimensional American options . Management Science , 50 : 1222 – 1234 .
  • Beibel , M. and Lerche , H.R. 1997 . A new look at optimal stopping problems related to mathematical finance . Statistica Sinica , 7 : 93 – 108 .
  • Bensoussan , A. 1984 . On the theory of option pricing . Acta Applicandae Mathematicae , 2 : 139 – 158 .
  • Bolia , N. , Glasserman , P. and Juneja , S. 2004 . “ Function-approximation-based importance sampling for pricing American options ” . In Proceedings of the 2004 Winter Simulation Conference 604 – 611 .
  • Carr , P. , Jarrow , R. and Myneni , R. 1992 . Alternative characterizations of American put options . Mathematical Finance , : 87 – 105 .
  • Chen, N. and Glasserman, P., 2005, Additive and multiplicative duals for American option pricing, Columbia Univversity Working paper.
  • Chiarella, C. and Ziogas, A., 2006, American call options on jump diffusion processes: a Fourier transform approach, Sidney University of Technology working paper.
  • Davis , M.H.A. and Karatzas , I. 1994 . “ A deterministic approach to optimal stopping ” . In Probability, Statistics and Optimisation , Edited by: Kelly , F.P. 455 – 466 . NewYork, Chichester : John Wiley and Sons .
  • Delbaen , F. and Yor , M. 2002 . Passport options . Mathematical Finance , 12 ( 4 ) : 299 – 328 .
  • Dellacherie , C. and Meyer , P.A. 1978 . Probabilities and Potential , North-Holland : Elsevier .
  • Detemple , J. , Feng , S. and Tian , W. 2003 . The valuation of American call options on the minimum of two dividend-paying assets . The Annals of Applied Probability , 13 ( 3 ) : 953 – 983 .
  • Elliott , R.J. 1982 . Stochastic Calculus and Applications , Berlin, New York : Springer .
  • El Karoui , N. and Quenez , M.C. 1995 . Dynamic programming and pricing of contingent claims in an incomplete market . SIAM Journal on Control and Optimization , 33 ( 1 ) : 29 – 66 .
  • Glasserman , P. 2003 . Monte Carlo Methods in Financial Engineering , Berlin-Heidelberg-New York : Springer .
  • Haugh , M. and Kogan , L. 2004 . Pricing American options: a dual approach . Operations Research , 52 : 258 – 270 .
  • Jacka , S.D. 1991 . Optimal stopping and the American put . Mathematical Finance , 2 : 1 – 14 .
  • Jacod , J. and Shiryaev , A.N. 2002 . Limit Theorems for Stochastic Processes , 2nd ed. , Berlin-Heidelberg-New York : Springer . Volume 288 of Grundlehren der mathematischen Wissenschaften,
  • Jaillet , P. , Lamberton , D. and Lapeyre , B. 1990 . Variational inequalities and the pricing of American options . Acta Applicandae Mathematicae , 21 : 263 – 289 .
  • Jamshidian , F. 1992 . An analysis of American options . Review of Future Studies , : 73 – 80 . Formulas for American options. Working paper, (1989)
  • Jamshidian, F., 2003, Linear invariant option pricing and application to American and Bermudan options, A collection of three working papers and two presentations substantially consolidated in this paper.
  • Joshi, M.S., 2006, A simple derivation of and improvements to Jamshidian's and Roger's upper bound method for Bermudan options, Working paper.
  • Joshi , M.S. and Theis , J. 2002 . Bounding Bermudan swaptions in a swap-rate market model . Quantitative Finance , 2 ( 5 ) : 370 – 377 .
  • Karatzas , I. 1988 . On the pricing of American options . Applied Mathematics and Optimization , 17 : 37 – 60 .
  • Kim , I.J. 1990 . The analytic valuation of American options . Review of Financial Studies , 3 : 545 – 572 .
  • Kolodko , A. and Schoenmakers , J. 2004 . Upper bounds for Bermudan style derivatives . Monte Carlo Methods and Applications , 10 : 331 – 343 .
  • Kolodko , A. and Schoenmakers , J. 2006 . Iterative construction of the optimal Bermudan stopping time . Finance and Stochastics , 10 : 27 – 49 .
  • Kramkov , D.O. 1996 . Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets . Probability Theory and Related Fields , 105 : 459 – 479 .
  • Lepeltier , J.P. 1984 . Mainguenau: le jeu de Dynkin en theorie generale sans L'hypothese de Mokobodski . Stochastics , 13 : 25 – 44 .
  • McKean , H.P. 1965 . Appendix: a free boundary problem for the heat equation arising from a problem of mathematical economics . Industrial Management Review , 6 ( 32–39 )
  • Protter , P. 2001 . A partial introduction to financial asset pricing theory . Stochastic Processes and Their Applications , 91 : 169 – 203 .
  • Rogers , L.C.G. 2002 . Monte Carlo valuation of American options . Mathematical Finance , 12 : 271 – 286 .
  • Shepp , L. and Shiryaev , A.N. 1993 . The Russian option: reduced regret . Annals of Applied Probability , 3 : 631 – 640 .
  • Shiryaev , A.N. 1963 . On optimum methods in quickest detection problems . Theory of Probability and its Applications , 8 : 22 – 46 .

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.