Pricing variable annuity with surrender guarantee

A variational inequality arising from optimal surrender of variable annuity with lookback benefit

“…In contrast to Bernard et al [1], the surrender benefit in their study is linked to the maximum value between the policyholder's account value and the guaranteed minimum accumulated benefit. Moreover, they show that the results in Jeon and Kwak [5] can be reduced to those in Bernard et al [1] under certain parameter conditions. The model in this paper can be considered as an extension of Jeon and Kwak [5] because the accumulated account value in the surrender benefit is replaced by a constant multiple of the maximum process of the policyholder's account value.…”

“…Moreover, they show that the results in Jeon and Kwak [5] can be reduced to those in Bernard et al [1] under certain parameter conditions. The model in this paper can be considered as an extension of Jeon and Kwak [5] because the accumulated account value in the surrender benefit is replaced by a constant multiple of the maximum process of the policyholder's account value.…”

“…There have been several studies on the optimal surrender strategies for VA contracts recently, such as Bernard et al [1], Shen et al [2], Kang and Ziveyi [3], and Jeon and Kwak [4,5]. In the baseline model of Bernard et al [1], the payoff at the maturity is the maximum of the policyholder's accumulated account value and a constant minimum guarantee.…”

“…Recently, Jeon and Kwak [5] investigated the VA contract with surrender guarantee. In contrast to Bernard et al [1], the surrender benefit in their study is linked to the maximum value between the policyholder's account value and the guaranteed minimum accumulated benefit.…”

“…To obtain a specific solution, we apply the recursive integration method proposed by Huang et al [14], solving the integral equation numerically. Jeon and Kwak [4,5] show the efficiency and accuracy of RIM by comparing benchmark values.…”