`Regression anytime' with brute-force SVD truncation
Bender,Christian Schweizer,Nikolaus
Bender,Christian
Schweizer,Nikolaus
Abstract
We propose a new least-squares Monte Carlo algorithm for the approximation of conditional expectations in the presence of stochastic derivative weights. The algorithm can serve as a building block for solving dynamic programming equations, which arise, for example, in nonlinear option pricing problems or in probabilistic discretization schemes for fully nonlinear parabolic partial differential equations. Our algorithm can be generically applied when the underlying dynamics stem from an Euler approximation to a stochastic differential equation. A built-in variance reduction ensures that the convergence in the number of samples to the true regression function takes place at an arbitrarily fast polynomial rate, if the problem under consideration is smooth enough.
Description
Date
2021-06
Journal Title
Journal ISSN
Volume Title
Publisher
Research Projects
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Journal Issue
Keywords
BSDEs, dynamic programming, Least-squares Monte Carlo, Monte Carlo simulation, quantitative finance, regression later, statistical learning
Citation
Bender, C & Schweizer, N 2021, '`Regression anytime' with brute-force SVD truncation', Annals of Applied Probability, vol. 31, no. 3, pp. 1140-1179. https://doi.org/10.1214/20-AAP1615