Risk-constrained portfolio choice under rank-dependent utility

We revisit the problem of portfolio choice for a rank-dependent utility maximiser in an arbitrage-free and complete market, subject to a budget constraint and a risk exposure constraint. We extend previous results in the literature by considering a general distortion risk measure for measuring risk exposure, which covers a wide range of popular risk measures such as value-at-risk, expected shortfall, spectral risk measures, etc. We first show that a solution exists for the portfolio selection problem with multiple constraints under general conditions. We provide a closed-form characterisation of optimal portfolios, all the while dispensing with extraneous monotonicity assumptions typically used in the literature. We then consider some important and economically relevant special cases of our general setup and provide illustrative numerical examples.