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Combined Derivative Estimators

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Advances in Modeling and Simulation

Abstract

We discuss combinations of simulation-based derivative estimators using infinitesimal perturbation analysis (IPA) and the likelihood ratio method (LRM). We first provide a historical perspective on combinations of IPA and LRM and then turn to connections with the generalized likelihood ratio (GLR) method. We re-derive a GLR estimator for barrier options through a combination of IPA and LRM. We then consider the behavior of a GLR estimator for a discrete-time approximation to a diffusion process as the time step shrinks. We show that an average of low-rank GLR estimators has a continuous-time limit, even though each individual estimator blows up. The limit matches an estimator previously derived through Malliavin calculus and also through a combination of IPA and LRM.

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Acknowledgements

I thank the editors for organizing this Festschrift and the reviewers for their helpful comments.

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Authors and Affiliations

  1. Columbia Business School, New York, NY, USA

    Paul Glasserman

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  1. Paul Glasserman
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Correspondence to Paul Glasserman .

Editor information

Editors and Affiliations

  1. Randwick, NSW, Australia

    Zdravko Botev

  2. NVIDIA, Berlin, Germany

    Alexander Keller

  3. University of Waterloo, Waterloo, ON, Canada

    Christiane Lemieux

  4. Rennes Bretagne-Atlantique, INRIA, Rennes Cedex, France

    Bruno Tuffin

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Glasserman, P. (2022). Combined Derivative Estimators. In: Botev, Z., Keller, A., Lemieux, C., Tuffin, B. (eds) Advances in Modeling and Simulation. Springer, Cham. https://doi.org/10.1007/978-3-031-10193-9_10

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