A primal-dual algorithm for BSDEs

Christian Bender, Nikolaus Schweizer, Jia Zhuo

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We generalize the primal–dual methodology, which is popular in the pricing of early-exercise options, to a backward dynamic programming equation associated with time discretization schemes of (reflected) backward stochastic differential equations (BSDEs). Taking as an input some approximate solution of the backward dynamic program, which was precomputed, e.g., by least-squares Monte Carlo, this methodology enables us to construct a confidence interval for the unknown true solution of the time-discretized (reflected) BSDE at time 0. We numerically demonstrate the practical applicability of our method in two 5-dimensional nonlinear pricing problems where tight price bounds were previously unavailable.
Original languageEnglish
Pages (from-to)866-901
JournalMathematical Finance
Volume27
Issue number3
DOIs
Publication statusPublished - 1 Jul 2017

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Reflected Backward Stochastic Differential Equation
Primal-dual Algorithm
Backward Stochastic Differential Equation
Pricing
Differential equations
Methodology
pricing
Discretization Scheme
Time Discretization
Dynamic programming
Exercise
Dynamic Programming
Confidence interval
Least Squares
Costs
Approximate Solution
methodology
Unknown
Generalise
programming

Cite this

Bender, Christian ; Schweizer, Nikolaus ; Zhuo, Jia. / A primal-dual algorithm for BSDEs. In: Mathematical Finance. 2017 ; Vol. 27, No. 3. pp. 866-901.
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A primal-dual algorithm for BSDEs. / Bender, Christian; Schweizer, Nikolaus; Zhuo, Jia.

In: Mathematical Finance, Vol. 27, No. 3, 01.07.2017, p. 866-901.

Research output: Contribution to journalArticleScientificpeer-review

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