The Optimal Decision Of Variable Annuity With Guaranteed Minimum Death Benefit Under Different Individual

Nowadays variable annuities are more and more popular all over the world, especially those variable annuities embedded variety of guarantees. Many previous literatures have investigated the mechanics of the guarantees and well described the evolution of the variable annuity. They usually apply risk-neutral pricing theory to price the embedded guaranteed options. Unfortunately, the prices of the guaranteed options under risk-neutral pricing theory are always higher than the market prices, this is a serious problem that we all should pay more attention to.In this paper, we mainly focus on the variable annuities with embedded guaranteed minimum death benefits and test the impacts of GMDB on the policyholders’ behaviors. We apply the utility-based dynamic model to describe the evolution of the variable an-nuity, and establish a trinomial tree from the terminal period to the initial period, then derive the optimal allocation and consumption through backward induction by making the utility value maximal at each period. Finally we utilize the Monte-Carlo simulation to price the GMDB under the optimal and rational behaviors.