Optimal investment strategies with a minimum performance constraint

We consider the optimal investment problem of a fund manager in the presence of a minimum
guarantee constraint on the fund performance. The manager receives a fee which is proportional
to the liquidation value of the portfolio or of the surplus over the guarantee in case it is positive
and zero otherwise, eventually augmented by a constant fee. Her remuneration is reduced through
the application of a penalty if the value of the fund at maturity is below a specied-in- advance
threshold (minimum guarantee). We deal with two dierent settings: a continuous time economy
with constant instantaneous interest rate and the case where the short-term interest rate evolves as
the Vasicek model. Explicit formulas for the optimal investment strategy are presented. We compare
our portfolio strategies to the Merton portfolio and to the Option Based Portfolio Insurance strategy.