Before revision: In this paper, we study a portfolio selection problem in which an agent trades a risk-free asset and multiple risky assets with deterministic mean return rates and volatility and wants to maximize the \alpha-quantile of her wealth at some terminal time . Because of the time inconsistency caused by quantiles, we consider intra-personal equilibrium strategies.
After revision: Although maximizing median and quantiles is intuitively appealing and has an axiomatic foundation, it is difficult to study the optimal portfolio strategy due to the discontinuity and time inconsistency in the objective function. We use the intra-personal equilibrium strategies.