First exit time probability for multidimensional diffusions: A PDE-based approach

✍ Scribed by P. Patie; C. Winter

• Book ID: 104005755
• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 648 KB
• Volume: 222
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2007.10.043

✦ Synopsis

First exit time distributions for multidimensional processes are key quantities in many areas of risk management and option pricing. The aim of this paper is to provide a flexible, fast and accurate algorithm for computing the probability of the first exit time from a bounded domain for multidimensional diffusions. First, we show that the probability distribution of this stopping time is the unique (weak) solution of a parabolic initial and boundary value problem. Then, we describe the algorithm which is based on a combination of the sparse tensor product finite element spaces and an hp-discontinuous Galerkin method. We illustrate our approach with several examples. We also compare the numerical results to classical Monte Carlo methods.