  Variable annuities, as a class of retirement income products, allow equity
market exposure for a policyholder's retirement fund with electable additional
guarantees to limit the downside risk of the market. Management fees and
guarantee insurance fees are charged respectively for the market exposure and
for the protection from the downside risk. We investigate the impact of
management fees on the pricing of variable annuity guarantees under optimal
withdrawal strategies. Two optimal strategies, from policyholder's and from
insurer's perspectives, are respectively formulated and the corresponding
pricing problems are solved using dynamic programming. Our results show that
when management fees are present, the two strategies can deviate significantly
from each other, leading to a substantial difference of the guarantee insurance
fees. This provides a possible explanation of lower guarantee insurance fees
observed in the market. Numerical experiments are conducted to illustrate our
results.
