Abstracts

Variable annuities play an increasingly important role in helping individual investors to achieve a secure retirement. The present work provides an analysis of the variable annuity policy. Especially, we focus on the valuation of the guaranteed minimum death benefits and the guaranteed minimum living benefits. We assume that the fee rate is fixed at the beginning of the contract. We then define and derive indifference fee rates for the insurer based on indifference pricing theory. It consists in solving two stochastic control problems. For that we apply recent results on backward stochastic differential equations with jumps and provide a verification theorem which gives the optimal strategy in each case. We numerically evaluate indifference fees, applying a Monte Carlo method and a dichotomy algorithm. We conclude our study with numerical illustrations of sensibilities of indifference fees with respect to parameters.