Optimal fee structure of variable annuities

Abstract We study the design of fee structures of variable annuities as a stochastic control problem, in which an insurer is allowed to choose the fee structure in any form that satisfies the budget constraint, and seeks an optimal one to maximize its business objective. Under the no surrender assumption, we show that the optimal fee structure is of barrier type with a time-dependent free boundary. The insurer's optimal strategy is to charge fees if and only if the account value of variable annuities hits the free boundary from below.