Geometric Learning and Filtering in Finance

We develop a method for incorporating relevant geometric information into a broad range of classical filtering and machine learning algorithms. We apply these techniques to approximate the solution of the non-Euclidean... [ view full abstract ]

We develop a method for incorporating relevant geometric information into a broad range of classical filtering and machine learning algorithms. We apply these techniques to approximate the solution of the non-Euclidean filtering problem to arbitrary precision. We then extend the particle filtering algorithm to compute our asymptotic solution to arbitrary precision.  The filtering techniques are applied to incorporate the non-Euclidean geometry present in stochastic volatility models, optimal Markowitz portfolios and the shape of the forward-rate.  We obtain improvements of principal component analysis and the improved algorithms can be used to parsimoniously estimate the evolution of the shape of forward-rate curves.