Developing a Model-free Data-driven Framework for Problems in Finance

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As the main source of quantitative, predictive data and information for financial institutions, models represent a critical aspect of the decision-making process. However, improper modeling assumptions can lead to poor business decisions and significant financial losses. The Basel Committee on Banking Supervision and the Federal Reserve explicitly require banks to introduce additional safeguards against model risk. The main objective of this research is to develop a model-free framework to explore the implied stochastic process in data, so that critical financial problems can be solved on a model-free basis. In this research, I will propose a discrete framework showing the implied stochastic process based on the real-world time series data. Our simple, efficient approach is different from other popular model-free approaches, as it uses artificial intelligence, doesn't require machine training and is insensitive to parameters or hyper parameters. It can be applied to solve a wide range of financial problems, from pricing and investment to risk management and capital allocation. The core research objectives are as follows. The first objective is to build the framework under various probability measures from the data set, and study the theoretical properties of the framework, such as time-consistency, convergence and stability. Secondly, I will study the methods for solving stochastic control problems in the framework without the restriction of stochastic models. Thus, the methods can be applied to portfolio optimization or decision-making problems in practice. Thirdly, I will explore the cross-sectional information between different data sets, such as S&P 500 index, VIX and their corresponding derivatives prices. This research will take these data sets as an example to study the lattice construction for S&P 500 index so as to simultaneously fit all these data sets. The results of this research will be a novel data-driven model-free discrete approach to explore the implied stochastic processes from real-world data. This research program is interdisciplinary in nature and represents a challenging intersection of mathematical modelling in economics, computational methods, data science and finance. Its anticipated outcome will reveal the implied stochastic process in the data with a novel model-free framework. It will also provide a model-free solution for people working in financial mathematics, the financial services industry (banks, insurance companies, pension funds) and financial regulation for their daily practice. Meanwhile, this program provides a complex training for students in theoretical knowledge and hands-on experiences.