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On the Neyman-Pearson problem for law-invariant risk measures and robust utility functionals

Please always quote using this URN:urn:nbn:de:0296-matheon-564
  • Motivated by optimal investment problems in mathematical finance, we consider a variational problem of Neyman-Pearson type for law-invariant robust utility functionals and convex risk measures. Explicit solutions are found for quantile-based coherent risk measures and related utility functionals. Typically, these solutions exhibit a critical phenomenon: If the capital constraint is below some critical value, then the solution will coincide with a classical solution; above this critical value, the solution is a superposition of a classical solution and a less risky or even risk-free investment. For general risk measures and utility functionals, it is shown that there exists a solution that can be written as a deterministic increasing function of the price density.

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Metadaten
Author:Alexander Schied
URN:urn:nbn:de:0296-matheon-564
Referee:Hans Föllmer
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2004/02/13
Release Date:2004/01/23
Institute:Humboldt-Universität zu Berlin
Technische Universität Berlin
Preprint Number:74
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