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

作为金融机构定量预测数据和信息的主要来源，模型是决策过程的一个关键方面。然而，不正确的建模假设可能会导致糟糕的业务决策和重大的财务损失。巴塞尔银行监管委员会和联邦明确要求银行针对模型风险引入额外的保障措施。本研究的主要目标是开发一个无模型框架，以探索数据中隐含的随机过程，从而可以在无模型的基础上解决关键的金融问题。 在这项研究中，我将提出一个离散的框架，显示隐含的随机过程的基础上，现实世界的时间序列数据。我们简单高效的方法与其他流行的无模型方法不同，因为它使用人工智能，不需要机器训练，对参数或超参数不敏感。它可以应用于解决广泛的金融问题，从定价和投资到风险管理和资本配置。 核心研究目标如下。第一个目标是从数据集中建立各种概率测度下的框架，并研究框架的理论性质，如时间一致性，收敛性和稳定性。其次，在不受随机模型约束的框架下研究随机控制问题的求解方法。因此，该方法可应用于实际的投资组合优化或决策问题。第三，探讨不同数据集之间的横截面信息，如标准普尔500指数，波动率指数及其相应的衍生品价格。本研究将以这些数据集为例，研究标准普尔500指数的格构，以同时拟合所有这些数据集。这项研究的结果将是一种新的数据驱动的无模型离散方法，探索隐含的随机过程，从现实世界的数据。 该研究计划是跨学科的，代表了经济学，计算方法，数据科学和金融数学建模的挑战性交叉。其预期结果将揭示隐含的随机过程中的数据与一个新的无模型的框架。它还将为从事金融数学、金融服务业（银行、保险公司、养老基金）和金融监管的人员提供无模型解决方案。同时，该计划为学生提供了理论知识和实践经验的综合培训。

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.