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.

本文调查了连续时间金融范式在投资组合选择和衍生品定价中的几个最重要的应用。虽然它承认范式为研究人员和从业者提供的强大见解，但它发现它引入的几种方法论方法本身已经固化为范式并变得功能失调。由于无法对现实世界的问题进行建模，他们降级并忽略了重要的现实问题，或者采用了与他们应该解决的问题几乎没有关系的简化方式。然后，该论文在所有情况下都提供了一种替代方法，该方法可以通过用数值估计和近似值代替数学优雅，通过严格的经济和数学推理达到所需的解决方案。