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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

On the structure of discounted optimal stopping problems for one-dimensional diffusions

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Pages 537-554 | Received 30 Sep 2009, Accepted 14 Oct 2010, Published online: 10 Oct 2011

References

  • Abramovitz , M. and Stegun , I.A. 1972 . Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , National Bureau of Standards New York : Wiley .
  • Alvarez , L.H.R. 2001 . Reward functionals, salvage values, and optimal stopping . Math. Methods Oper. Res. , 54 : 315 – 337 .
  • Alvarez , L.H.R. 2008 . A class of solvable stopping games . Appl. Math. Optim. , 49 : 265 – 295 .
  • Bateman , H. and Erdélyi , A. 1953 . Higher Transcendental Functions , New York : McGraw-Hill .
  • Beibel , M. and Lerche , H.R. 1997 . A new look at optimal stopping problems related to mathematical finance . Stat. Sinica , 7 : 93 – 108 .
  • Beibel , M. and Lerche , H.R. 2000 . A note on optimal stopping of regular diffusions under random discounting . Theory Probab. Appl. , 45 : 657 – 669 .
  • Bensoussan , A. and Lions , J.L. 1982 . Applications of Variational Inequalities in Stochastic Control , Amsterdam : North Holland .
  • Borodin , A.N. and Salminen , P. 2002 . Handbook of Brownian Motion , 2nd ed. , Basel : Birkhäuser .
  • Broadie , M. and Detemple , J. 1995 . American capped call options on dividend-paying assets . Rev. Financial Stud. , 8 : 161 – 191 .
  • Christensen , S. and Irle , A. 2011 . A harmonic function technique for the optimal stopping of diffusions . Stochastics , 83 ( 4–6 ) : 347 – 363 .
  • Dayanik , S. and Karatzas , I. 2003 . On the optimal stopping problem for one-dimensional diffusions . Stochastic Process. Appl. , 107 : 173 – 212 .
  • Dynkin , E.B. 1963 . The optimum choice of the instant for stopping a Markov process . Soviet Math. Dokl. , 4 : 627 – 629 .
  • Fakeev , A.G. 1970 . Optimal stopping rules for stochastic processes with continuous parameter . Theory Probab. Appl. , 15 : 324 – 331 .
  • Gapeev , P.V. 2005 . “ The spread option optimal stopping game ” . In Exotic Option Pricing and Advanced Levy Models , Edited by: Kyprianou , A. , Schoutens , W. and Wilmott , P. 293 – 305 . Chichester : Wiley .
  • Itô , K. and McKean , H.P. 1965 . Diffusion Processes and Their Sample Paths , Berlin : Springer .
  • Karatzas , I. and Shreve , S.E. 1991 . Brownian Motion and Stochastic Calculus , 2nd ed. , New York : Springer .
  • Karlin , S. and Taylor , H.M. 1981 . A Second Course in Stochastic Processes , London/New York : Academic Press .
  • Kramkov , D.O. and Mordecki , E. 1994 . Integral option . Theory Probab. Appl. , 39 ( 1 ) : 201 – 211 .
  • D. Lamberton and M. Zervos, On the problem of optimally stopping a one-dimensional Itô diffusion, Preprint (2006)
  • Lerche , H.R. and Urusov , M. 2007 . Optimal stopping via measure transformation: The Beibel–Lerche approach . Stochastics , 79 ( 3–4 ) : 275 – 291 .
  • McKean , H.P. 1965 . Appendix: A free boundary problem for the heat equation arising from a problem of mathematical economics . Indust. Manag. Rev. , 6 : 32 – 39 .
  • Mucci , A.G. 1978 . Existence and explicit determination of optimal stopping times . Stochastic Process. Appl. , 8 : 33 – 58 .
  • Øksendal , B. 1998 . Stochastic Differential Equations: An Introduction with Applications , 5th ed. , Berlin : Springer .
  • Øksendal , B. and Reikvam , K. 1998 . Viscosity solutions of optimal stopping problems . Stochastics Stochastics Rep. , 62 : 285 – 301 .
  • Peskir , G. 2005 . A change-of-variable formula with local time on curves . J. Theoret. Probab. , 18 : 499 – 535 .
  • Peskir , G. 2007 . “ A change-of-variable formula with local time on surfaces ” . In Séminaire de Probababilité XL , Lecture Notes in Mathematics Vol. 1899 , 69 – 96 . Springer .
  • Peskir , G. and Shiryaev , A.N. 2006 . Optimal Stopping and Free-Boundary Problems , Basel : Birkhäuser .
  • Revuz , D. and Yor , M. 1999 . Continuous Martingales and Brownian Motion , 3rd ed. , Berlin : Springer .
  • Rogers , L.C.G. and Williams , D. 1987 . Diffusions, Markov Processes and Martingales II. Itô Calculus , New York : Wiley .
  • Salminen , P. 1985 . Optimal stopping of one-dimensional diffusions . Math. Nachr. , 124 : 85 – 101 .
  • Shepp , L.A. and Shiryaev , A.N. 1994 . A new look at the pricing of Russian options . Theory Probab. Appl. , 39 ( 1 ) : 103 – 119 .
  • Shiryaev , A.N. 1978 . Optimal Stopping Rules , Berlin : Springer .
  • Shiryaev , A.N. 1999 . Essentials of Stochastic Finance , Singapore : World Scientific .
  • Snell , J.L. 1952 . Applications of martingale system theorems . Trans. Amer. Math. Soc. , 73 : 293 – 312 .

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