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Solving optimal stopping problems of linear diffusions by applying convolution approximations

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  • Luis H. R. Alvarez

Abstract

We study how the convolution approximation of continuous mappings can be applied in solving optimal stopping problems of linear diffusions whenever the underlying payoff is not differentiable and the smooth fit principle does not necessarily apply. We construct a sequence of smooth reward functions converging uniformly on compacts to the original reward and, consequently, we derive a sequence of continuously differentiable (i.e. satisfying the smooth fit principle) value functions converging to the value of the original stopping problem. Copyright Springer-Verlag Berlin Heidelberg 2001

Suggested Citation

  • Luis H. R. Alvarez, 2001. "Solving optimal stopping problems of linear diffusions by applying convolution approximations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 53(1), pages 89-99, April.
    • Handle: RePEc:spr:mathme:v:53:y:2001:i:1:p:89-99
    DOI: 10.1007/s001860000098
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    Citations

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    Cited by:

    1. Alvarez, Luis H. R. & Koskela, Erkki, 2005. "Wicksellian theory of forest rotation under interest rate variability," Journal of Economic Dynamics and Control, Elsevier, vol. 29(3), pages 529-545, March.
    2. Rutger-Jan Lange & Coen Teulings, 2018. "The option value of vacant land and the optimal timing of city extensions," Tinbergen Institute Discussion Papers 18-033/III, Tinbergen Institute.
    3. Erhan Bayraktar, 2007. "A Proof of the Smoothness of the Finite Time Horizon American Put Option for Jump Diffusions," Papers math/0703782, arXiv.org, revised Dec 2008.
    4. Pui Chan Lon & Mihail Zervos, 2011. "A Model for Optimally Advertising and Launching a Product," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 363-376, May.

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