PhD Project: Non-Linear Least Square Monte-Carlo Algorithms
The Least Square Monte-Carlo Alogorithm is a broadly used algorithm used to price bermudean options. It relies on an approximation of the continuation value by orthogonal projection on a linear subspace spanned by chosen basis functions. A key ingredient in the success of this method is the fact that the orthogonal projection on a linear space can be directly computed by a matrix inversion. The project is to perform the projection on a non linear subset, i.e. when one tries to approximate the value function with a set of functions that depend non-linearly of a finite number of parameter. One of the key to the success of this approach, is to solve efficiently a complex optimization problem, similar to those encountered in neural networks.
Keywords: Least-Square Monte-Carlo, Stochastic Calculus, Black-Scholes equation, Computational Optimization.
Applications can be made by selecting the below link.
Please attach supporting documentation including a covering letter outlining why you would like to undertake the PhD project and a current CV including 2 referees. Please note that more than one application can be made if you wish to be considered for more than one PhD project.