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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 79, 2007 - Issue 3-4: Special issue on optimal stopping with applications
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Original Articles

Linear programming approach to the optimal stopping of singular stochastic processes

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Pages 309-335 | Received 08 May 2006, Accepted 22 Aug 2006, Published online: 05 Nov 2008

References

  • Bhatt , A.G. and Borkar , V.S. 1996 . Occupation measures for controlled Markov processes: characterization and optimality . Annals of Probability , 24 : 1531 – 1562 .
  • Cho , M.J. and Stockbridge , R.H. 2002 . Linear programming formulation for optimal stopping problems . SIAM Journal on Control and Optimization , 40 : 1965 – 1982 .
  • Ethier , S.N. and Kurtz , T.G. 1986 . Markov Processes: Characterization and Convergence , New York, NY : Wiley .
  • Feller , W. 1965 . An Introduction to Probability Theory and its Applications , Vol. 2 , New York : Wiley .
  • Graverson , S.E. and Peskir , G . 1997 . On the Russian option: the expected waiting time . Theory of Probability and its Applications , 42 : 564 – 575 .
  • Hausdorff , F. 1923 . Momentprobleme f r ein endliches Intervall . Mathematische Zeitschrift , 16 : 220 – 248 .
  • Helmes , K. 2002 . “ Numerical methods for optimal stopping using linear and nonlinear programming ” . In Stochastic Theory and Control , Edited by: Pasik-Duncan , B. Vol. 280 , 185 – 203 . Berlin : Springer-Verlag .
  • Helmes, K. and R hl, S., A geometrical characterization of the multi-dimensional Hausdorff and dale polytopes with applications to exit time problems, preprint.
  • Hernandez-Lerma , O. and Lasserre , J.B. 1996 . Discrete-time Markov Control Processes: Basic Optimality Criteria , New York : Springer .
  • Hernandez-Lerma , O. and Lasserre , B. 1998 . Approximation schemes for infinite linear programs . SIAM Journal on Optimization , 8 : 973 – 988 .
  • Hernandez-Lerma , O. and Lasserre , J.B. 1999 . Further Topics on Discrete-Time Markov Control Processes , New York : Springer .
  • Karatzas , I. and Shreve , S.E. 1996 . Brownian Motion and Stochastic Calculus , 2nd ed. , New York : Springer-Verlag .
  • Kurtz , T.G. and Stockbridge , R.H. 1998 . Existence of Markov controls and characterization of optimal Markov controls . SIAM Journal on Control and Optimization , 36 : 609 – 653 .
  • Kurtz , T.G. and Stockbridge , R.H. 2001 . Stationary solutions and forward equations for controlled and singular martingale problems . Electronic Journal of Probability , 6 : 1 – 52 . Paper No. 14,
  • Manne , A.S. 1960 . Linear programming and sequential decisions . Management Science , 6 : 259 – 267 .
  • B. 1998 . Stochastic Differential Equations , 5th ed. , Berlin : Springer-Verlag . ksendal
  • Peskir , G. 2005 . The Russian option: Finite horizon . Finance Stoch. , 9 : 251 – 267 .
  • Shepp , L.A. and Shiryaev , A.N. 1993 . A new look at pricing of the ‘Russian option’ . Theory of Probability and its Applications , 39 : 103 – 119 .
  • Shreve , S.E. 1988 . “ An introduction to singular stochastic control ” . In Stochastic Differential Systems, Stochastic Control Theory and Applications (Minneapolis, Minn., 1986) , Vol. 10 , 513 – 528 . New York–Berlin : Springer . IMA Vol. Math. Appl.,
  • Stockbridge , R.H. 1990 . Time-average control of martingale problems: existence of a stationary solution . Annals of Probability , 18 : 190 – 205 .
  • Stockbridge , R.H. 1990 . Time-average control of martingale problems: a linear programming formulation . Annals of Probability , 18 : 206 – 217 .
  • Young , L.C. 1933 . On approximation by polygons in the calculus of variations . Proceeding of Royal Society, Series A , 141 : 325 – 341 .

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