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`Regression Anytime' with Brute-Force SVD Truncation

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  • Christian Bender
  • Nikolaus Schweizer

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, e.g., in non-linear option pricing problems or in probabilistic discretization schemes for fully non-linear 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.

Suggested Citation

  • Christian Bender & Nikolaus Schweizer, 2019. "`Regression Anytime' with Brute-Force SVD Truncation," Papers 1908.08264, arXiv.org, revised Oct 2020.
    • Handle: RePEc:arx:papers:1908.08264
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    References listed on IDEAS

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    Cited by:

    1. Vikranth Lokeshwar & Vikram Bhardawaj & Shashi Jain, 2019. "Neural network for pricing and universal static hedging of contingent claims," Papers 1911.11362, arXiv.org.

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