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，模型代表了决策过程的一个关键方面。然而，不恰当的建模假设可能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（Basel Committee on Banking Supervision）和美联储（fed）明确要求银行引入额外的防范模型风险的措施。本研究的主要目的是建立一个无模型的框架来探索数据中隐含的随机过程，从而在无模型的基础上解决关键的金融问题。在这项研究中，我将提出一个离散框架，显示基于现实世界时间序列数据的隐含随机过程。我们简单、高效的方法不同于其他流行的无模型方法，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构建各种概率测度下的框架，并研究框架的时间一致性、收敛性和稳定性等理论性质。其次，我将研究在不受随机模型限制的框架下求解随机控制问题的方法。因此，该方法可以应用于实际的投资组合优化或决策问题。第三，我将探索不同数据集之间的横截面信息，如标准普尔500指数、VIX及其对应的衍生品价格。本研究将以这些数据集为例，研究标准普尔500指数的格结构，以便同时拟合所有这些数据集。本研究的结果将是一种新的数据驱动的无模型离散方法，用于探索现实世界数据中的隐含随机过程。这个研究项目本质上是跨学科的，代表了经济学、计算方法、数据科学和金融中数学建模的一个具有挑战性的交叉点。其预期结果将以一种新颖的无模型框架揭示数据中隐含的随机过程。它还将为从事金融数学、金融服务行业（银行、保险公司、养老基金）和金融监管工作的人们提供一个无模型的解决方案，用于他们的日常实践。同时，该项目为学生提供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.