Work

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

Year: 2004

Type: article

Abstract: 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.

Source: The Annals of Applied Probability

DOI: 10.1214/105051604000000341

Author: Alexander Schied

Institution: Technische Universität Berlin

Language: English

Topic: Risk and Portfolio Optimization

Subfield: Management Science and Operations Research

Field: Decision Sciences

Domain: Social Sciences

Open Access status: bronze

Funders: Deutsche Forschungsgemeinschaft, University of British Columbia

OpenAlex ID: W1968514970