I examine a class of utility maximization problems with a not necessarily lawinvariant utility, and with a not necessarily law-invariant risk measure constraint. The objective function is an integral of some function U with respect to some probability measure P, and the constraint set contains...

I examine a class of utility maximization problems with a not necessarily law-invariant utility, and with a not necessarily law-invariant risk measure constraint. The objective function is a Lebesgue integral of some function U with respect to some probability measure P, and the constraint set...

Empirical evidence suggests that ambiguity is prevalent in insurance pricing and underwriting, and that often insurers tend to exhibit more ambiguity than the insured individuals (e.g., Hogarth and Kunreuther (1989)). Motivated by these findings, we consider a problem of demand for insurance...