Thesis Abstract

Abstract
The utilization of differential equations in financial mathematics has gained significant attention in recent years due to the complexity and dynamics of financial markets. This thesis explores the various applications of differential equations in modeling and analyzing financial phenomena. The study begins with an introduction that provides an overview of the importance of differential equations in financial mathematics, followed by a discussion on the background of the study, problem statement, objectives, limitations, scope, significance, and the structure of the thesis. Chapter Two presents a comprehensive literature review that examines existing studies and research on the application of differential equations in financial mathematics. The review covers various aspects such as option pricing models, interest rate modeling, stochastic calculus, and risk management strategies. It also explores the historical development of differential equations in financial mathematics and highlights key contributions in the field. Chapter Three focuses on the research methodology employed in this study. The chapter outlines the research design, data collection methods, sampling techniques, and analytical tools used to investigate the applications of differential equations in financial mathematics. It also discusses the theoretical framework guiding the research process and the rationale behind the chosen methodology. Chapter Four presents an in-depth discussion of the findings obtained from the application of differential equations in financial mathematics. The chapter explores the effectiveness of various differential equation models in predicting asset prices, analyzing market trends, and managing financial risks. It also discusses the limitations and challenges encountered in applying differential equations to financial problems and proposes potential areas for future research. Finally, Chapter Five offers a conclusion and summary of the thesis, highlighting the key findings, implications, and contributions to the field of financial mathematics. The chapter discusses the significance of the research findings, recommendations for practitioners and policymakers, and suggestions for further research in the area of differential equations in financial mathematics. Overall, this thesis provides valuable insights into the applications of differential equations in financial mathematics, shedding light on the potential benefits and challenges associated with using these mathematical tools in analyzing and managing financial assets. By bridging the gap between theory and practice, this study contributes to the advancement of knowledge in financial mathematics and offers practical implications for industry professionals and researchers alike.

Thesis Overview

The project titled "Applications of Differential Equations in Financial Mathematics" aims to explore the practical applications of differential equations in the field of financial mathematics. Differential equations are powerful mathematical tools that describe the rate of change of various quantities over time. In the context of financial mathematics, these equations can be used to model and analyze complex financial systems, such as stock prices, interest rates, and option pricing. The research will begin with an introduction that provides background information on both differential equations and financial mathematics. The problem statement will highlight the importance of understanding the underlying mathematical principles governing financial systems. The objectives of the study will be clearly defined, outlining the specific goals and outcomes that the research aims to achieve. The study will also discuss the limitations and scope of the research, acknowledging the constraints and boundaries within which the study will operate. The significance of the study will be emphasized, highlighting the potential impact of applying differential equations in financial mathematics to enhance decision-making processes and risk management strategies in the financial industry. The structure of the thesis will be outlined to provide a roadmap for the reader, guiding them through the various chapters and sections of the research. Definitions of key terms and concepts will be provided to ensure clarity and understanding for readers unfamiliar with the subject matter. The literature review will delve into existing research and studies related to the application of differential equations in financial mathematics. This section will provide a comprehensive overview of the current state of knowledge in the field, identifying gaps and opportunities for further research. The research methodology will detail the approach and methods used to conduct the study, including data collection, analysis techniques, and modeling strategies. Various mathematical models and tools for solving differential equations will be discussed, highlighting their relevance and applicability in financial mathematics. The findings of the study will be presented and discussed in detail, showcasing the practical applications of differential equations in analyzing financial data and making informed decisions. The discussion will explore the implications of the findings, their relevance to real-world financial scenarios, and potential areas for future research and development. Finally, the conclusion will summarize the key findings and insights of the research, drawing implications for the field of financial mathematics. The research overview will highlight the significance of the study in advancing our understanding of how differential equations can be applied to solve complex financial problems and inform decision-making processes in the financial industry.