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On the feasibility of portfolio optimization under expected shortfall. (English) Zbl 1190.91116

Summary: We address the problem of portfolio optimization under the simplest coherent risk measure, i.e. the expected shortfall. As is well known, one can map this problem into a linear programming setting. For some values of the external parameters, when the available time series is too short, portfolio optimization is ill-posed because it leads to unbounded positions, infinitely short on some assets and infinitely long on others. As first observed by Kondor and coworkers, this phenomenon is actually a phase transition. We investigate the nature of this transition by means of a replica approach.

MSC:

91B80 Applications of statistical and quantum mechanics to economics (econophysics)
91G10 Portfolio theory
82C99 Time-dependent statistical mechanics (dynamic and nonequilibrium)
91B84 Economic time series analysis
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