Faculty of Actuarial Science and Insurance Seminar with Elisa Mastrogiacomo

We consider the optimal strategy problem of a fund manager in the presence of a minimum
guarantee. The manager, in fact, receives a fee which is proportional to the liquidation value of the
portfolio, reduced through the application of a penalty if the liquidation value is below a specified-

in-advance threshold (minimum guarantee). We deal with two different settings: a continuous time
economy with constant instantaneous interest rate and the case where the short-term interest rate is

described by the Vasicek model. Explicit formulas for the optimal investment are presented; moreover,
we analyze the sensitivity of the optimal investment strategy with respect to the different model's
parameters. We then compare our portfolio strategies with the Merton portfolio and with the Option
Based Insurance strategy (see El Karoui et. al. 2005).