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Conditional Monte Carlo Learning for Diffusions II: extended methodology and application to risk measures and early stopping problems

Abstract : In Conditional Monte Carlo Learning for Diffusions part I (CMCLDI) [2], we presented a One-layered Nested Monte Carlo (1NMC) to simulate functionals U of a Markov process X. Based on a judicious combination between regression and 1NMC used for localization purpose, this methodology allows to simulate U_{t≥s} conditionally on X{s}. The parallel suitability and scalability of 1NMC makes this algorithm very competitive to simulate quantities that are almost impossible to simulate with other methods. In this paper, using the double layer of trajectories, we explain further the mathematical background of the control on the bias propagation. With this double layer structure, we also detail how to adjust the variance to get a better approximation of the second moment from the regression. In normal and log-normal models, this variance adjustment allows a better description of tail events. Since we applied this algorithm on Backward Stochastic Differential Equations in CMCLDI, we show here its strength for the simulation of risk measures and optimal stopping problems. Two highly dimensional numerical examples are executed in few minutes on one Graphics Processing Unit (GPU).
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https://hal.archives-ouvertes.fr/hal-02959494
Contributor : Lokman Abbas-Turki <>
Submitted on : Tuesday, October 6, 2020 - 9:04:43 PM
Last modification on : Wednesday, June 2, 2021 - 4:26:36 PM
Long-term archiving on: : Thursday, January 7, 2021 - 7:30:25 PM

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  • HAL Id : hal-02959494, version 1

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Lokman Abbas-Turki, G. Pagès, Babacar Diallo. Conditional Monte Carlo Learning for Diffusions II: extended methodology and application to risk measures and early stopping problems. 2020. ⟨hal-02959494⟩

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