  We revisit two classical problems: the determination of the law of the
underlying with respect to a risk-neutral measure on the basis of option
prices, and the pricing of options with convex payoffs in terms of prices of
call options with the same maturity (all options are European). The formulation
of both problems is expressed in a language loosely inspired by the theory of
inverse problems, and several proofs of the corresponding solutions are
provided that do not rely on any special assumptions on the law of the
underlying and that may, in some cases, extend results currently available in
the literature.
