Risk-constrained portfolio choice under rank-dependent utility

Mario Ghossoub () and Michael Boyuan Zhu ()
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Mario Ghossoub: University of Waterloo
Michael Boyuan Zhu: University of Waterloo

Finance and Stochastics, 2025, vol. 29, issue 2, No 3, 399-442

Abstract: Abstract 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.

Keywords: Portfolio choice; Rank-dependent utility; Quantile formulation; Choquet integral; Distortion risk measures; 91B42; 91G10; 91G20; 91G70; 28A12 (search for similar items in EconPapers)
JEL-codes: C61 D89 D90 G11 G40 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00780-024-00555-z

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