From innovation to obfuscation: continuous time finance fifty years later

This paper surveys several of the most important applications of the continuous time finance paradigm in portfolio selection and derivatives pricing. While it recognizes the powerful insights that the paradigm offered to researchers and practitioners, it finds that several methodological approaches that it introduced have themselves hardened into paradigms and become dysfunctional. They have downgraded and neglected significant real-world problems because of their inability to model them, or adopted simplifications that had little relevance to the problems that they were supposed to solve. The paper then offers in all cases an alternative methodology that can reach the desired solution via rigorous economic and mathematical reasoning, by replacing mathematical elegance with numerical estimations and approximations.