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Pathwise Dynamic Programming

Author

Listed:
  • Christian Bender

    (Department of Mathematics, Saarland University, Postfach 151150, D-66041 Saarbrücken, Germany)

  • Christian Gärtner

    (Department of Mathematics, Saarland University, Postfach 151150, D-66041 Saarbrücken, Germany)

  • Nikolaus Schweizer

    (Department of Econometrics and Operations Research, Tilburg University, NL-5000 LE Tilburg, Netherlands)

Abstract

We present a novel method for deriving tight Monte Carlo confidence intervals for solutions of stochastic dynamic programming equations. Taking some approximate solution to the equation as an input, we construct pathwise recursions with a known bias. Suitably coupling the recursions for lower and upper bounds ensures that the method is applicable even when the dynamic program does not satisfy a comparison principle. We apply our method to three nonlinear option pricing problems, pricing under bilateral counterparty risk, under uncertain volatility, and under negotiated collateralization.

Suggested Citation

  • Christian Bender & Christian Gärtner & Nikolaus Schweizer, 2018. "Pathwise Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 965-965, August.
    • Handle: RePEc:inm:ormoor:v:43:y:2018:i:3:p:965-965
    DOI: 10.1287/moor.2017.0891
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    References listed on IDEAS

    as
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