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Stochastic efficiency and inefficiency in portfolio optimization with incomplete information: a set-valued probability approach

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Abstract

In this paper we extend the notion of stochastic efficiency and inefficiency in portfolio optimization to the case of incomplete information by means of set-valued probabilities. The notion of set-valued probability models the concept of incomplete information about the underlying probability space and the probability associated with each scenario. Unlike other approaches in literature, our notion of inefficiency is introduced by means of the Monge–Kantorovich metric. We provide some numerical examples to illustrate this approach.

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Acknowledgements

The second author (FM) was partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) in the form of a Discovery Grant (2019-05237).

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Authors and Affiliations

  1. SKEMA Business School, Université Côte d’Azur, Sophia Antipolis Campus, Sophia Antipolis, France

    D. La Torre

  2. Department of Mathematics and Statistics, Acadia University, Wolfville, NS, Canada

    F. Mendivil

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  1. D. La Torre
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  2. F. Mendivil
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Correspondence to D. La Torre.

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La Torre, D., Mendivil, F. Stochastic efficiency and inefficiency in portfolio optimization with incomplete information: a set-valued probability approach. Ann Oper Res 311, 1085–1098 (2022). https://doi.org/10.1007/s10479-020-03886-0

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  • DOI: https://doi.org/10.1007/s10479-020-03886-0

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