Pathwise dynamic programming

Christian Bender, Christian Gärtner, Nikolaus Schweizer

Research output: Contribution to journalArticleScientificpeer-review

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.
Original languageEnglish
Pages (from-to)965-995
JournalMathematics of Operations Research
Volume43
Issue number3
DOIs
Publication statusPublished - Aug 2018

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Dynamic programming
Dynamic Programming
Recursion
Stochastic Dynamic Programming
Costs
Comparison Principle
Option Pricing
Volatility
Pricing
Confidence interval
Upper and Lower Bounds
Approximate Solution

Keywords

  • stochastic dynamic programming
  • Monte Carlo
  • confidence bounds
  • option pricing

Cite this

Bender, Christian ; Gärtner, Christian ; Schweizer, Nikolaus. / Pathwise dynamic programming. In: Mathematics of Operations Research. 2018 ; Vol. 43, No. 3. pp. 965-995.
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Pathwise dynamic programming. / Bender, Christian; Gärtner, Christian; Schweizer, Nikolaus.

In: Mathematics of Operations Research, Vol. 43, No. 3, 08.2018, p. 965-995.

Research output: Contribution to journalArticleScientificpeer-review

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AB - 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.

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