ABSTRACT
In the first part of this work, we study a particular class of infinite dimensional linear
programs on the value of a function at a given number of points, with the additional
constraint that this function be convex. Convexity is shown to be the key ingredient
making these problems tractable. We detail some applications, with a particular focus
on arbitrage constraints between call options.
In the second part, we use the results of chapter one to compute tractable relaxations
to some multivariate or basket option pricing problems. We then derive tight
price bounds on basket options in some particular cases.
Finally, part three uses some recent results in moment theory and semidefinite
programming to refine the convex relaxation techniques of part two and compute
tighter constraints linking the prices of basket options.