ON THE SOLUTION UNIQUENESS IN PORTFOLIO OPTIMIZATION AND RISK ANALYSIS

Bogdan Grechuk (), Andrzej Palczewski () and Jan Palczewski
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Bogdan Grechuk: Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK
Andrzej Palczewski: Faculty of Mathematics, University of Warsaw, Banacha 2, Warsaw 02-097, Poland
Jan Palczewski: School of Mathematics, University of Leeds, Leeds LS2 9JT, UK

International Journal of Theoretical and Applied Finance (IJTAF), 2024, vol. 27, issue 05n06, 1-27

Abstract: In this paper, we consider the issue of solution uniqueness of the mean-deviation portfolio optimization problem and its inverse for asset returns distributed over a finite number of scenarios. Due to the asymmetry of returns, the risk is assessed by a general deviation measure introduced by Rockafellar et al. [(2006b) Optimality conditions in portfolio analysis with general deviation measures, Mathematical Programming 108, 515–540] instead of the standard deviation as in the classical Markowitz optimization problem. We demonstrate that, in general, one cannot expect the uniqueness of Pareto-optimal profit sharing in cooperative investment and the uniqueness of solutions in the mean-deviation Black–Litterman asset allocation model. For a large class of deviation measures, we provide a resolution of the above nonuniqueness issues based on the principle of law-invariance. We provide several examples illustrating the nonuniqueness and the law-invariant solution.

Keywords: Portfolio optimization; cooperative investment; Black–Litterman model (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0219024924500195

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