Balancing growth and shortfall probability in continuous time active portfolio management

Active portfolio management is concerned with objectives related to the outperformance of the return of a target benchmark portfolio. Here we consider an objective that relates the probability of achieving a given performance objective to the time it takes to achieve the objective, in this way balancing risk and return. As a special case, our analysis includes the case where the investor wants to minimize the expected time until a given performance goal is reached subject to a constraint on the shortfall probability. We find that this purely probabilistic based objective is equivalent to maximizing a Hyperbolic Absolute Risk Aversion utility function with particular parameter values, thus extending the class of equivalences between utility (i.e. subjective) and probabilistic (i.e. objective) based portfolio optimization.