Arbitrage-Free Regularization

We introduce a path-dependent geometric framework which generalizes the HJM modeling approach to a wide variety of other asset classes. A machine learning regularization framework is developed with the objective of removing... [ view full abstract ]

We introduce a path-dependent geometric framework which generalizes the HJM modeling approach to a wide variety of other asset classes. A machine learning regularization framework is developed with the objective of removing arbitrage opportunities from models within this general framework. The regularization method relies on minimal deformations of a model subject to a path-dependent penalty that detects arbitrage opportunities. We prove that the solution of this regularization problem is independent of the arbitrage-penalty chosen, subject to a fixed information loss functional. This paper is focused on placing machine learning methods in finance on a sound theoretical basis.