Applications of Differential Equations in Financial Mathematics

Thesis Abstract

Abstract
This thesis explores the applications of differential equations in the field of financial mathematics, focusing on how these mathematical tools can be utilized to model and analyze various financial phenomena. The study begins by providing an overview of the background of differential equations and their relevance to financial mathematics. It then presents the problem statement, outlining the challenges and gaps in existing research that this study aims to address. The objectives of the study are clearly defined, highlighting the specific goals and outcomes that the research seeks to achieve. The limitations and scope of the study are also discussed, setting boundaries on the extent and depth of the research. The significance of the study is emphasized, emphasizing the potential impact and contributions of the findings to both the academic and practical aspects of financial mathematics. The structure of the thesis is outlined to provide a roadmap for the reader, guiding them through the organization and flow of the research document. In the literature review chapter, ten key topics related to the applications of differential equations in financial mathematics are explored in depth. This section provides a comprehensive overview of existing research, theories, and methodologies in the field, offering a foundation for the subsequent chapters. The research methodology chapter details the approach, methods, and tools used in conducting the study. Eight key components of the research methodology are discussed, including data collection, analysis techniques, and modeling strategies. The chapter elucidates the rationale behind the chosen methodologies and justifies their suitability for the study. In the discussion of findings chapter, the research outcomes are presented and analyzed in detail. The implications of the findings are discussed, and their relevance to the field of financial mathematics is examined. The chapter also highlights any patterns, trends, or insights that emerged from the analysis, contributing to the body of knowledge in the field. Finally, the conclusion and summary chapter provide a holistic overview of the study, summarizing the key findings, implications, and contributions of the research. The conclusions drawn from the study are discussed, and recommendations for future research are provided. The chapter concludes with a reflection on the significance of the study and its potential impact on the field of financial mathematics. In summary, this thesis offers a comprehensive exploration of the applications of differential equations in financial mathematics, presenting a detailed analysis of the theoretical foundations, methodological approaches, and practical implications of using these mathematical tools in the financial domain. The research contributes to the advancement of knowledge in the field and provides valuable insights for researchers, practitioners, and educators interested in the intersection of mathematics and finance.