Semi-Smooth Newton Methods for Black-Scholes with American Options and Portfolio Optimization Problems

Efficient numerical solutions of several important partial-differential equation based models in mathematical finance are impeded by the fact that they contain operators which are Lipschitz continuous but not continuously differentiable. As a consequence, Newton methods are not directly applicable and, more importantly, do not provide their typical fast convergence properties.

In this talk semi-smooth Newton methods are presented as a remedy to the the above-mentioned difficulties. We also discuss algorithmic issues including the primal-dual active set strategy and path following techniques.