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Conference on the Effective Use of High Performance Workstations In Scientific Computing
August 4-6, 2008
Unviersity of Toronto
Toronto, Canada

Organizers
W.H. Enright, C.C. Christara, and K.R. Jackson (University of Toronto)

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A Numerical Scheme for the Impulse Control Formulation for Pricing Variable Annuities with a Guaranteed Minimum Withdrawal Benefit (GMWB)
by
Peter Forsyth
University of Waterloo
Coauthors: Zhuliang Chen

In this paper, we outline an impulse stochastic control formulation for pricing variable annuities with a Guaranteed Minimum Withdrawal Benefit (GMWB) assuming the policyholder is allowed to withdraw funds continuously. We develop a numerical scheme for solving the Hamilton-Jacobi-Bellman (HJB) variational inequality corresponding to the impulse control problem. We prove the convergence of our scheme to the viscosity solution of the continuous withdrawal problem, provided a strong comparison result holds. The scheme can be easily generalized to price discrete withdrawal contracts. Numerical experiments are conducted, which show a region where the optimal control appears to be non-unique.

Date received: May 21, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawv-04.