In this section we study the problem of maximizing the expected utility
under a given budget constraint in a broader context. The random variables X will vary in a general convex class X ⊂ L0(Ω,F, P) of admissible payoff profiles. In the setting of our financial market model, this will allow us to explain the demand for nonlinear payoff profiles provided by financial derivatives.
In order to formulate the budget constraint in this general context, we introduce a linear pricing rule of the form
where P∗ is a probability ...