A numerical scheme for the impulse control formulation for pricing variable annuities with a guaranteed minimum withdrawal benefit (GMWB)
نویسندگان
چکیده
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 single numerical scheme for solving the Hamilton-Jacobi-Bellman (HJB) variational inequality corresponding to the impulse control problem, and for pricing realistic discrete withdrawal contracts. We prove the convergence of our scheme to the viscosity solution of the continuous withdrawal problem, provided a strong comparison result holds. The convergence to the viscosity solution is also proved for the discrete withdrawal case. Numerical experiments are conducted, which show a region where the optimal control appears to be non-unique.
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عنوان ژورنال:
- Numerische Mathematik
دوره 109 شماره
صفحات -
تاریخ انتشار 2008