Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext. 32700
Fax: 519-746-4319
PDF files require Adobe Acrobat Reader
MC 6460
An Zhou
Department of Applied Mathematics, University of Waterloo
Structured Reverse Mode Automatic Differentiation in Nested Monte Carlo Simulations
In many practical large scale computational problems, the calculation of partial derivatives of the object function f with respect to input parameters are entailed and the dimension of inputs n is much larger the one of outputs m. The use of reverse mode automatic differentiation (AD) is mostly efficient as it computes the gradient in the same amount of runtime as f regardless of the input dimension n. However, it demands excessive memory. To enjoy the runtime efficiency of reverse mode without paying unaffordable memory, structured reverse mode has been proposed and succeeded in several applications. Due to the fundamental difficulty in automatic structure detection, structured reverse mode has not been fully automated. This thesis, instead of trying to solve to structure detection problem for a completely generic piece of code, is devoted to the analysis and implementation of deploying structured reverse mode to a generic class of problems with a known structure, nested Monte Carlo simulations. We reveal the general structure pattern of Monte Carlo simulations in financial applications. Space/time tradeoff on deploying structured reverse mode is discussed in details and numerical experiments using Variable Annuity program are conducted to corroborate the analysis. Significant memory and runtime reductions are observed. We argue such contribution is important as nested Monte Carlo simulations accommodates several large scale computations in financial services that are crucial in practice.
Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext. 32700
Fax: 519-746-4319
PDF files require Adobe Acrobat Reader
The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is co-ordinated within the Office of Indigenous Relations.