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Portfolio construction based on stochastic dominance and target return distributions

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Abstract

Mean-risk models have been widely used in portfolio optimization. However, such models may produce portfolios that are dominated with respect to second order stochastic dominance and therefore not optimal for rational and risk-averse investors. This paper considers the problem of constructing a portfolio which is non-dominated with respect to second order stochastic dominance and whose return distribution has specified desirable properties. The problem is multi-objective and is transformed into a single objective problem by using the reference point method, in which target levels, known as aspiration points, are specified for the objective functions. A model is proposed in which the aspiration points relate to ordered outcomes for the portfolio return. This concept is extended by additionally specifying reservation points, which act pre-emptively in the optimization model. The theoretical properties of the models are studied. The performance of the models on real data drawn from the Hang Seng index is also investigated.

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Authors and Affiliations

  1. CARISMA: The Centre for the Analysis of Risk and Optimisation Modelling Applications, School of Information Systems, Computing and Mathematics, Brunel University, Uxbridge, Middlesex, UB8 3PH, UK

    Diana Roman, Ken Darby-Dowman & Gautam Mitra

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  1. Diana Roman
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  2. Ken Darby-Dowman
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  3. Gautam Mitra
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Correspondence to Gautam Mitra.

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Roman, D., Darby-Dowman, K. & Mitra, G. Portfolio construction based on stochastic dominance and target return distributions. Math. Program. 108, 541–569 (2006). https://doi.org/10.1007/s10107-006-0722-8

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  • DOI: https://doi.org/10.1007/s10107-006-0722-8

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