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Optimal stopping in Hilbert spaces and pricing of American options

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Abstract.

We consider an optimal stopping problem for a Hilbert-space valued diffusion. We prove that the value function of the problem is the unique viscosity solution of an obstacle problem for the associated parabolic partial differential equation in the Hilbert space. The results are applied to investigate the pricing of American interest rate options in the lognormal Heath-Jarrow-Morton model of yield curve dynamics.

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Authors and Affiliations

  1. BRE Bank SA, ul. Senatorska 18, 00-950 Warszawa, Poland, , , , , , PL

    Dariusz Gatarek

  2. School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA (e-mail: swiech@math.gatech.edu), , , , , , GE

    Andrzej ŚwiechRID="*"ID="*"  Andrzej Świ&ecedil;ch was partially supported by NSF grant DMS-9706760

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  1. Dariusz Gatarek
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  2. Andrzej ŚwiechRID="*"ID="*"  Andrzej Świ&ecedil;ch was partially supported by NSF grant DMS-9706760
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Manuscript received: October 1998

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ID="*"  Andrzej Świ&ecedil;ch was partially supported by NSF grant DMS-9706760

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Gatarek, D., ŚwiechRID="*"ID="*"  Andrzej Świ&ecedil;ch was partially supported by NSF grant DMS-9706760, A. Optimal stopping in Hilbert spaces and pricing of American options. Mathematical Methods of OR 50, 135–147 (1999). https://doi.org/10.1007/s001860050040

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  • DOI: https://doi.org/10.1007/s001860050040

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