Abstract
We provide analytical results for a static portfolio optimization problem with two coherent risk measures. The use of two risk measures is motivated by joint decision-making for portfolio selection where the risk perception of the portfolio manager is of primary concern, hence, it appears in the objective function, and the risk perception of an external authority needs to be taken into account as well, which appears in the form of a risk constraint. The problem covers the risk minimization problem with an expected return constraint and the expected return maximization problem with a risk constraint, as special cases. For the general case of an arbitrary joint distribution for the asset returns, under certain conditions, we characterize the optimal portfolio as the optimal Lagrange multiplier associated to an equality-constrained dual problem. Then, we consider the special case of Gaussian returns for which it is possible to identify all cases where an optimal solution exists and to give an explicit formula for the optimal portfolio whenever it exists.
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Acknowledgements
We are grateful to Oya Ekin Karaşan for her continuous support at the early stages of the project. In addition, we would like to thank two anonymous referees whose comments motivated us for much of the developments in Sect. 3.
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Aktürk, T.D., Ararat, Ç. Portfolio optimization with two coherent risk measures. J Glob Optim 78, 597–626 (2020). https://doi.org/10.1007/s10898-020-00922-y
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DOI: https://doi.org/10.1007/s10898-020-00922-y