Bounding the generalized convex call price

The present article introduces the concept of generalized calls (options whose value at expiry can be any function of the difference between the price of the underlying security and the striking price) and presents some of the properties of such options through the use of absence of stochastic dominance arguments. It deals with bounding relations of call premium applied to generalized options of the convex type, i.e. nonlinear convex options. These relations are obtained from the hypothesis of absence of second-order stochastic dominance between comparable strategies and without any hypothesis on the underlying security's distribution. The article presents economic justification of this method, some classical lemmas about stochastic dominance, and some bounds for convex calls.