PeGASUS aims at developing approximate and random geometric algorithms with applications in finance, and related open source software.

Research focuses on:

• a) classical problems of computational geometry, functional analysis and machine learning, such as volume computation in high dimensions (100 to 1000) and clustering; and
• b) in two modern finance problems, portfolio optimization and financial crises prediction.

Finance applications with geometric representation of stock markets reveal problems on volume computation and sampling of convex and non-convex bodies in high dimensions, as well as demanding clustering problems of joint distributions.

Project objectives are the development of novel methods for computing volumes in high dimensions and new clustering techniques, that can be applied to financial problems, especially with large stock markets which was impossible with the existing methods.