Stochastic Automatic Differentiation: Efficient Tapeless Implementation of Automatic Differentiation for Monte-Carlo Simulations

Posted: 1 Aug 2017

See all articles by Christian P. Fries

Christian P. Fries

Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics; DZ Bank AG

Stefan Sedlmair

Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics

Date Written: July 27, 2017

Abstract

In this paper we present an efficient implementation of automatic differentiations of random variables (see https://ssrn.com/abstract=2995695).

Using this implementation can increase the speed of the calculation of the automatic differentiation and reduce the memory requirements.

In some cases this approach may give surprising results: We give examples where the the calculation of all partial derivatives is 10000-times faster compared to the calculation of the value and the memory footprint is the same. A trivial example is the AAD calculation of a sum of random variables. While this is an operator on a random variable (i.e., a vector of thousands of Monte-Carlo samples), the partial derivatives are just scalars.

Keywords: Automatic Differentiation, Adjoint Automatic Differentiation Monte Carlo Simulation, Object Oriented Implementation

JEL Classification: C15, G13

Suggested Citation

Fries, Christian P. and Sedlmair, Stefan, Stochastic Automatic Differentiation: Efficient Tapeless Implementation of Automatic Differentiation for Monte-Carlo Simulations (July 27, 2017). Available at SSRN: https://ssrn.com/abstract=3010912

Christian P. Fries (Contact Author)

Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics ( email )

Theresienstrasse 39
Munich
Germany

DZ Bank AG ( email )

60265 Frankfurt am Main
Germany

Stefan Sedlmair

Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics ( email )

Theresienstrasse 39
Munich
Germany

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