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Table of Contents:

Chapter One: Introduction
1.1 Background of the Study
1.2 Problem Statement
1.3 Research Questions
1.4 Objectives of the Study
1.5 Significance of the Study
1.6 Limitations of the Study
1.7 Scope of the Study

Chapter Two: Literature Review
2.1 Overview of Stochastic Calculus
2.2 Itoʼs Lemma
2.3 Stochastic Differential Equations
2.4 Applications of Stochastic Calculus in Finance

Chapter Three: Research Methodology
3.1 Research Design
3.2 Data Collection Methods
3.3 Data Analysis Techniques
3.4 Sampling Techniques
3.5 Research Instruments

Chapter Four: Discussion of Findings
4.1 Analysis of Results
4.2 Comparison with Existing Literature
4.3 Implications of Findings
4.4 Recommendations for Future Research

Chapter Five: Conclusion and Summary
5.1 Summary of Key Findings
5.2 Conclusion
5.3 Contributions to the Field
5.4 Recommendations for Practitioners
5.5 Suggestions for Future Research

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Thesis Overview:

Stochastic calculus is a branch of mathematics that deals with the study of random processes and their evolution over time. One of the fundamental results in stochastic calculus is Itoʼs Lemma, which provides a framework for the analysis of stochastic differential equations. This thesis focuses on exploring the concepts of Itoʼs Lemma and stochastic differential equations, and their applications in finance.

The introduction sets the stage for the study by providing background information on stochastic calculus and outlining the problem statement and research questions. The objective of the study is to analyze the application of Itoʼs Lemma and stochastic differential equations in financial modeling.

Chapter two reviews the existing literature on stochastic calculus, Itoʼs Lemma, and stochastic differential equations. It provides a comprehensive overview of the theoretical framework and practical applications of these concepts in finance.

Chapter three describes the research methodology employed in the study, including research design, data collection methods, and data analysis techniques. The chapter also discusses sampling techniques and research instruments used in the study.

In chapter four, the findings of the study are discussed and analyzed. The results are compared with existing literature, and the implications of the findings are discussed. Recommendations for future research in the field are also provided.

Finally, chapter five presents the conclusion and summary of the study. Key findings are summarized, conclusions are drawn, and contributions to the field are highlighted. Recommendations for practitioners and suggestions for future research are also included.

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