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.
Author: | Alexander Schied |
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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 |