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      Arbitrage-Free Regularization

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          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. In addition to the general properties of the minimal deformation, we also consider several explicit examples. This paper is focused on placing machine learning methods in finance on a sound theoretical basis and the techniques developed to achieve this objective may be of interest in other areas of application.

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          Theory of reproducing kernels

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            Sur les variétés à connexion affine, et la théorie de la relativité généralisée (première partie) (Suite)

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              Forecasting the term structure of government bond yields

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                Author and article information

                Journal
                13 October 2017
                Article
                1710.05114
                abe3e4b1-055b-4514-a092-bc395adb583d

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                91G30, 91G20, 68T05, 65J20, 60D05, 94A15
                37 pages
                q-fin.MF math.PR q-fin.PR stat.ML

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