Iterative improvement of lower and upper bounds for backward SDEs

Christian Bender, Christian Gärtner, Nikolaus Schweizer

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We introduce a novel numerical approach for a class of stochastic dynamic programs which arise as discretizations of backward stochastic differential equations or semilinear partial differential equations. Solving such dynamic programs numerically requires the approximation of nested conditional expectations, i.e., iterated integrals of previous approximations. Our approach allows us to compute and iteratively improve upper and lower bounds on the true solution, starting from an arbitrary and possibly crude input approximation. We demonstrate the benefits of our approach in a high-dimensional financial application.
Original languageEnglish
Pages (from-to)B442-B466
JournalSIAM Journal on Scientific Computing
Volume39
Issue number2
DOIs
Publication statusPublished - 1 Jan 2017

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Upper and Lower Bounds
Approximation
Iterated integral
Partial differential equations
Semilinear Differential Equations
Backward Stochastic Differential Equation
Differential equations
Conditional Expectation
Stochastic Dynamics
High-dimensional
Partial differential equation
Discretization
Arbitrary
Demonstrate
Class

Keywords

  • backward stochastic differential equations
  • dynamic programming
  • iterated improvement
  • Monte Carlo

Cite this

Bender, Christian ; Gärtner, Christian ; Schweizer, Nikolaus. / Iterative improvement of lower and upper bounds for backward SDEs. In: SIAM Journal on Scientific Computing. 2017 ; Vol. 39, No. 2. pp. B442-B466.
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Iterative improvement of lower and upper bounds for backward SDEs. / Bender, Christian; Gärtner, Christian; Schweizer, Nikolaus.

In: SIAM Journal on Scientific Computing, Vol. 39, No. 2, 01.01.2017, p. B442-B466.

Research output: Contribution to journalArticleScientificpeer-review

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