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August 2004 On the Neyman–Pearson problem for law-invariant risk measures and robust utility functionals
Alexander Schied
Ann. Appl. Probab. 14(3): 1398-1423 (August 2004). DOI: 10.1214/105051604000000341


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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Alexander Schied. "On the Neyman–Pearson problem for law-invariant risk measures and robust utility functionals." Ann. Appl. Probab. 14 (3) 1398 - 1423, August 2004.


Published: August 2004
First available in Project Euclid: 13 July 2004

zbMATH: 1121.91054
MathSciNet: MR2071428
Digital Object Identifier: 10.1214/105051604000000341

Primary: 62G10 , 91B28 , 91B30

Keywords: generalized moment problem , law-invariant risk measure , Neyman–Pearson problem , optimal contingent claim , robust utility functional

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.14 • No. 3 • August 2004
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