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A numerical scheme for the impulse control formulation for pricing variable annuities with a guaranteed minimum withdrawal benefit (GMWB)

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Abstract

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.

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Authors and Affiliations

  1. David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, Canada, N2L 3G1

    Zhuliang Chen & Peter A. Forsyth

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  1. Zhuliang Chen
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  2. Peter A. Forsyth
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Correspondence to Peter A. Forsyth.

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Chen, Z., Forsyth, P.A. A numerical scheme for the impulse control formulation for pricing variable annuities with a guaranteed minimum withdrawal benefit (GMWB). Numer. Math. 109, 535–569 (2008). https://doi.org/10.1007/s00211-008-0152-z

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  • DOI: https://doi.org/10.1007/s00211-008-0152-z

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