Shape Constrained Optimization, with Applications in Finance and Engineering

• TITLE: Shape Constrained Optimization, with Applications in Finance and Engineering.

• AUTHORS: Alexandre d'Aspremont

• INSTITUTION: Stanford University

• ADVISOR: Stephen Boyd

• STATUS: Degree Conferred Jun. 2004.

• FULL TEXT: Shape Constrained Optimization, with Applications in Finance and Engineering.

• 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