### Abstract

Original language | English |
---|---|

Pages (from-to) | 866-901 |

Journal | Mathematical Finance |

Volume | 27 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Jul 2017 |

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*Mathematical Finance*,

*27*(3), 866-901. https://doi.org/10.1111/mafi.12100

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*Mathematical Finance*, vol. 27, no. 3, pp. 866-901. https://doi.org/10.1111/mafi.12100

**A primal-dual algorithm for BSDEs.** / Bender, Christian; Schweizer, Nikolaus; Zhuo, Jia.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - A primal-dual algorithm for BSDEs

AU - Bender, Christian

AU - Schweizer, Nikolaus

AU - Zhuo, Jia

PY - 2017/7/1

Y1 - 2017/7/1

N2 - 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.

AB - 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.

U2 - 10.1111/mafi.12100

DO - 10.1111/mafi.12100

M3 - Article

VL - 27

SP - 866

EP - 901

JO - Mathematical Finance

JF - Mathematical Finance

SN - 0960-1627

IS - 3

ER -