Optimal Multiple Stopping of Linear Diffusions

Published Online:https://doi.org/10.1287/moor.1070.0301

References

  • Abramowitz M., Stegun I. A.Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (1984) (A Wiley-Interscience Publication, John Wiley & Sons, New York) . Reprint of 1972 ed. Selected Government Publications. MR 85j:00005aGoogle Scholar
  • Alvarez L. H. R., Shepp L. A. Optimal harvesting of stochastically fluctuating populations. J. Math. Biol. (1998) 37(2):155–177MR 99m:90047CrossrefGoogle Scholar
  • Barlow M. T. A diffusion model for electricity prices. Math. Finance (2002) 12(4):287–298CrossrefGoogle Scholar
  • Boetius F. Bounded variation singular stochastic control and associated Dynkin game. Trends in Mathematics (2001) 2000 Workshop of the Mathematical Finance Research ProjectKonstanz, Germany(Birkhäuser Verlag, Basel, Switzerland) 111–120MR1882823 (2002m:49044)Google Scholar
  • Boetius F., Kohlmann M. Connections between optimal stopping and singular stochastic control. Stochastic Process. Appl. (1998) 77(2):253–281MR1649007 (99g:93085)CrossrefGoogle Scholar
  • Borodin A. N., Salminen P.Handbook of Brownian Motion—Facts and Formulae, Probability and Its Applications (2002) 2nd ed.(Birkhäuser Verlag, Basel, Switzerland) . MR1912205CrossrefGoogle Scholar
  • Cadenillas A., Elliott R. J., Léger L. A. On the pricing of American options when the asset follows a mean-reverting process. (2002) . Preprint, University of Alberta, Edmonton, CanadaGoogle Scholar
  • Cairoli R., Dalang R. C. Sequential stochastic optimization. Wiley Series in Probability and Statistics: Probability and Statistics (1996) (Wiley-Interscience. John Wiley & Sons, New York) . MR1369770 (97d:60078)Google Scholar
  • Carmona R., Ludkovski M. Valuation of energy storage: An optimal switching approach. (2007) . Submitted for publicationGoogle Scholar
  • Carmona R., Ludkovski M. Pricing asset scheduling flexibility using optimal switching. Appl. Math. Finance (2008) . ForthcomingCrossrefGoogle Scholar
  • Carmona R., Touzi N. Optimal multiple stopping and valuation of swing options. Math. Finance (2008) 18(2):239–268CrossrefGoogle Scholar
  • Dayanik S. Optimal stopping of linear diffusions with random discounting. Math. Oper. Res. (2008) . Forthcoming. http://www.princeton.edu/∼sdayanik/papers/additive.pdfLinkGoogle Scholar
  • Dayanik S., Karatzas I. On the optimal stopping problem for one-dimensional diffusions. Stochastic Process. Appl. (2003) 107(2):173–212CrossrefGoogle Scholar
  • Dixit A. K., Pindyck R. S.Investment under Uncertainty (1994) (Princeton University Press, Princeton, NJ) CrossrefGoogle Scholar
  • Fakeev A. G. Optimal stopping of a Markov process. Theory Probab. Appl. (1971) 16:694–696MR 45:1249CrossrefGoogle Scholar
  • Itô K., McKean H. P.Diffusion Processes and Their Sample Paths (1974) (Springer-Verlag, Berlin) . MR 49:9963Google Scholar
  • Jaillet P., Ronn E. I., Tompaidis S. Valuation of commodity-based swing options. Management Sci. (2004) 50(7):909–921LinkGoogle Scholar
  • Karatzas I., Shreve S. E. Connections between optimal stopping and singular stochastic control. I. Monotone follower problems. SIAM J. Control Optim. (1984) 22(6):856–877MR762624 (87h:93075a)CrossrefGoogle Scholar
  • Karatzas I., Shreve S. E. Connections between optimal stopping and singular stochastic control. II. Reflected follower problems. SIAM J. Control Optim. (1985) 23(3):433–451MR784579 (87h:93075b)CrossrefGoogle Scholar
  • Karatzas I., Shreve S. E.Brownian Motion and Stochastic Calculus (1991) (Springer-Verlag, New York) . MR 92h:60127Google Scholar
  • Karatzas I., Shreve S. E.Methods of Mathematical Finance (1998) (Springer-Verlag, New York) . MR 2000e:91076CrossrefGoogle Scholar
  • Karlin S., Taylor H. M.A Second Course in Stochastic Processes (1981) (Academic Press [Harcourt Brace Jovanovich Publishers], New York) . MR 82j:60003Google Scholar
  • Lebedev N. N.Special Functions and Their Applications (1972) revised ed.(Dover Publications, New York) . R. A. Silverman, Frans. (Russian) and ed. Unabridged and corrected republication. MR 50:2568Google Scholar
  • Leung T., Sircar R. Accounting for risk aversion, vesting, job termination risk and multiple exercises in valuation of employee stock options. Math. Finance (2008) . ForthcomingGoogle Scholar
  • Mandelbaum A., Shepp L. A., Vanderbei R. J. Optimal switching between a pair of Brownian motions. Ann. Probab. (1990) 18(3):1010–1033MR1062057 (91i:60208)CrossrefGoogle Scholar
  • Mandelbaum A., Vanderbei R. J. Optimal stopping and supermartingales over partially ordered sets. Z. Wahrsch. Verw. Gebiete (1981) 57(2):253–264MR626819 (82k:60098)CrossrefGoogle Scholar
  • Mandelbaum A., Vanderbei R. J. Brownian bandits. The Dynkin Festschrift, Progr. Probab. (1994) 34(Birkhäuser Boston, Boston) 267–285MR1311725 (96k:60209)CrossrefGoogle Scholar
  • Meinshausen N., Hambly B. M. Monte Carlo methods for the valuation of multiple exercise options. Math. Finance (2004) 14:557–583CrossrefGoogle Scholar
  • Schwartz E. The stochastic behavior of commodity prices: Implications for valuation and hedging. J. Finance (1997) 52(3):923–973CrossrefGoogle Scholar
  • Shiryaev A. N.Optimal Stopping Rules (1978) (Springer-Verlag, New York) . MR 57:7906Google Scholar
  • Sircar R., Xiong W. A general framework for evaluating executive stock options. J. Econom. Dynam. Control (2007) 31(7):2317–2349CrossrefGoogle Scholar
  • Yushkevich A. A. Optimal switching problem for countable Markov chains: Average reward criterion. Math. Methods Oper. Res. (2001) 53(1):1–24MR1825245 (2002b:60120)CrossrefGoogle Scholar
  • Yushkevich A. A. Optimal switching problem for Markov chains. Markov Processes and Controlled Markov Chains (2002) (Kluwer Academic Publishers, Dordrecht, The Netherlands) 255–286MR2022430 (2005b:60111). [International Workshop on Markov Processes and Controlled Markov Chains. Changsha, China, 1999.]CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.