Pricing guaranteed minimum withdrawal benefits in variable annuities

Abstract

Variable annuities with Guaranteed Minimum Withdrawal Benefits (GMWB) are financial contracts between policyholders and insurance companies . A GMWB contract involves payment of a lump sum to the issuers from the investors. The money collected is then invested on some specially selected assets. The investors can withdraw up to a specified contractual rate each year, regardless of the performance of the investment. The holder may also withdraw more than the contractual amount with penalty. In this thesis, we consider both the continuous model and the discrete one. The continuous GMWB problem is modeled using singular control approach. Finite difference method with penalty approximation is used to calculate the contract value. In order to allow discrete withdrawals and incorporate some more complex features, we also consider the discrete case. The effects of various parameters are also considered. The study of optimal withdrawal strategies is carried out at the end.