We study the problem of active portfolio management where an investor seeks to minimise risk while attaining probabilistic constraint on terminal wealth (i.e., has an aspiration criterion) as well as a budget constraint; specifically, we consider investors with rank dependent expected utility preferences. We show that, in a general class of market models, the problem admits a quantile formulation and further that the optimal quantile can be characterized explicitly through the notion of isotonic projections. Moreover, we develop a risk-aware reinforcement learning methodology that employs a deep policy gradient framework to approximate the optimal strategy and illustrate the results for a variety of risk profiles and aspiration criteria.