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.
@article{1089736290,
author = {Schied, Alexander},
title = {On the Neyman--Pearson problem for law-invariant risk measures and robust utility functionals},
journal = {Ann. Appl. Probab.},
volume = {14},
number = {1},
year = {2004},
pages = { 1398-1423},
language = {en},
url = {http://dml.mathdoc.fr/item/1089736290}
}
Schied, Alexander. On the Neyman–Pearson problem for law-invariant risk measures and robust utility functionals. Ann. Appl. Probab., Tome 14 (2004) no. 1, pp. 1398-1423. http://gdmltest.u-ga.fr/item/1089736290/