A policyholder's utility indifference valuation model for the guaranteed annuity option

Insurance companies often include very long-term guarantees in participating life insurance products, which can turn out to be very valuable. Under a guaranteed annuity options (G.A.O), the insurer guarantees to convert a policyholder's accumulated funds to a life annuity at a fixed rated when the policy matures. Both financial and actuarial approaches have been used to valuate of such options. In the present work, we present an indifference valuation model for the guaranteed annuity option. We are interested in the additional lump sum that the policyholder is willing to pay in order to have the option to convert the accumulated funds into a lifelong annuity at a guaranteed rate.