Structure of Optimal Stopping Strategies for American Type Options

  • Alexander G. Kukush
  • Dmitrii S. Silvestrov
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 49)


The general pricing processes represented by an inhomogeneous vector Markov process with discrete time is considered. Its first component is interpreted as a price process and the second one as an index process controlling the price component. American type options with convex pay-off functions are studied. The structure optimal and ε-optimal buyer stopping strategies is investigated for various classes of convex pay-off functions.

Key words and phrases

Markov process optimal stopping convex pay-off function American options 

AMS 1991 subject classification

Primary 62P05 90C40 Secondary 60J25 60J20 


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  1. [1]
    Duffie, D. (1996). Dynamical Asset Pricing Theory. Princeton University Press.Google Scholar
  2. [2]
    Numerical Methods in Finance. (1998). Ed. by L.G.G. Rogers and D.Talay. Cambridge University Press.Google Scholar
  3. [3]
    Oksendal, B. (1992). Stochastic Differential Equations: An Introduction with Applications. Springer.Google Scholar
  4. [4]
    Karatzas, I. and Shreve, S. E. (1998). Methods of Mathematical Finance. Springer Verlag.zbMATHGoogle Scholar
  5. [5]
    Kukush, A. G. and Silvestrov, D. S. (1999). Optimal stopping strategies for American type options with discrete and continuous time. Theory Stoch. Procès. 5(21), 1–2, 71–79. In Proceedings of the Second International School on Actuarial and Financial Mathematics, Kiev, 1999.Google Scholar
  6. [6]
    Kukush, A.G. and Silvestrov, D.S. (2000). Optimal pricing of American type options with discrete time. Research Report 2000–1, Department of Mathematics and Physics, Mälardalen University.Google Scholar
  7. [7]
    Pliska, S.R. (1997). Introduction to Mathematical Finance. Blackwell.Google Scholar
  8. [8]
    Shiryaev, A.N. (1978).Optimal Stopping Rules. Springer.zbMATHGoogle Scholar
  9. [9]
    Shiryaev, A.N., Kabanov, Yu.M., Kramkov, D.O., and Mel’nikov, A.V. (1994). Toward a theory of pricing options of European and American types. I. Discrete time. Theory Probab. Appl. 39, 14–60.MathSciNetCrossRefGoogle Scholar
  10. [10]
    Silvestrov, D. S., Galochkin, V. G. and Sibirtsev, V. G. (1999). Algorithms and programs for optimal Monte Carlo pricing of American type options. Theory Stoch. Procès. 5(21),1–2, 175–187. In Proceedings of the Second International School on Actuarial and Financial Mathematics, Kiev, 1999.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Alexander G. Kukush
    • 1
  • Dmitrii S. Silvestrov
    • 2
  1. 1.Department of Mechanics and MathematicsKiev Taras Shevchenko UniversityKievUkraine
  2. 2.Department of Mathematics and PhysicsMälardalen UniversityVästeråsSweden

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