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On the Approximation of Infinite Dimensional Optimal Stopping Problems with Application to Mathematical Finance

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Abstract

We consider the approximation of the optimal stopping problem for infinite dimensional processes by variational methods. To this end, we employ a Fourier-Legendre representation for the state space and exhaust an indexed family of regularized Hamilton-Jacobi characterizations. We implement our results utilizing penalization and a method-of-lines semi-implicit finite element method; application to term-structure valuation problems from mathematical finance demonstrate the applicability of the approach.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Nevada, Las Vegas, 89154-4020, Las Vegas, NV, USA

    Michael D. Marcozzi

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  1. Michael D. Marcozzi
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Correspondence to Michael D. Marcozzi.

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This research was supported by the U.S. National Science Foundation, award number DMI-0422985.

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Marcozzi, M.D. On the Approximation of Infinite Dimensional Optimal Stopping Problems with Application to Mathematical Finance. J Sci Comput 34, 287–307 (2008). https://doi.org/10.1007/s10915-007-9168-2

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  • DOI: https://doi.org/10.1007/s10915-007-9168-2

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