Thesis Abstract

Abstract
The use of partial differential equations (PDEs) in finance has gained significant attention in recent years due to their effectiveness in modeling complex financial systems and phenomena. This thesis explores the applications of PDEs in finance, focusing on their role in pricing financial derivatives, risk management, and portfolio optimization. The study begins by providing an overview of PDEs and their relevance to financial modeling, highlighting their ability to capture the dynamic nature of financial markets. The literature review in this thesis examines existing research on the applications of PDEs in finance, discussing various numerical methods and techniques used to solve PDEs in financial modeling. The review also explores the challenges and limitations associated with using PDEs in finance, emphasizing the need for accurate and efficient numerical solutions to complex financial problems. The research methodology section outlines the approach taken to analyze the applications of PDEs in finance, including the selection of financial models, data sources, and numerical methods used in the study. The methodology also discusses the validation of the model results and the sensitivity analysis conducted to assess the robustness of the findings. The findings section presents a detailed discussion of the applications of PDEs in finance, highlighting their impact on pricing financial derivatives, managing risk, and optimizing investment portfolios. The results demonstrate the effectiveness of PDEs in capturing the dynamics of financial markets and their ability to provide valuable insights for decision-making in finance. In conclusion, this thesis summarizes the key findings and implications of using PDEs in finance, emphasizing their role in enhancing the accuracy and efficiency of financial modeling. The study highlights the importance of considering the dynamic nature of financial markets and the need for advanced mathematical tools, such as PDEs, to address complex financial problems effectively. Overall, this thesis contributes to the growing body of research on the applications of PDEs in finance, providing valuable insights into their use in pricing financial derivatives, risk management, and portfolio optimization. The findings of this study have implications for practitioners and researchers in the field of finance, offering new perspectives on how PDEs can be leveraged to improve decision-making and enhance financial performance.

Thesis Overview

The project titled "Applications of Partial Differential Equations in Finance" aims to explore the utilization of partial differential equations (PDEs) in the field of finance. This research overview provides a comprehensive insight into the significance and potential applications of incorporating PDEs in financial modeling and analysis. Chapter One of the thesis sets the foundation for the study by introducing the research topic, presenting the background of the study, stating the problem statement, defining the objectives, highlighting limitations and scope, emphasizing the significance of the study, and outlining the structure of the thesis. This chapter also includes the definition of key terms to establish a common understanding for readers. Chapter Two delves into a thorough literature review that encompasses ten key areas related to the applications of PDEs in finance. This section critically examines existing research, theories, and practices to provide a comprehensive understanding of the current state of knowledge in this field. Chapter Three focuses on the research methodology, detailing the approach, design, data collection methods, sampling techniques, and data analysis procedures employed in the study. This chapter also discusses the theoretical framework guiding the research and justifies the chosen methodology for investigating the application of PDEs in financial contexts. Chapter Four presents a detailed discussion of the findings derived from the application of PDEs in finance. This section analyzes the results obtained through the research methodology and interprets their implications for financial modeling, risk management, pricing strategies, and other relevant areas within the finance domain. Finally, Chapter Five serves as the conclusion and summary of the thesis. This section consolidates the key findings, highlights the contributions of the study to the field of finance, discusses the implications of the research outcomes, and provides recommendations for future research directions. The conclusion emphasizes the significance of incorporating PDEs in financial applications and underscores the potential benefits of utilizing advanced mathematical tools in financial decision-making processes. Overall, the project on "Applications of Partial Differential Equations in Finance" aims to bridge the gap between theoretical mathematical models and practical financial applications, offering valuable insights into the integration of PDEs in enhancing financial analysis, risk assessment, and decision-making processes within the dynamic landscape of the financial industry.