ANALYSIS OF FINITE HORIZON INVESTMENT STRATEGIES FOR A LOGARITHMIC UTILITY FUNCTION
ABSTRACT
We considered a simple optimization problem for an investor whose actions cannot affect the market prices and have no other profit than the returns on financial investments. Under general conditions on the nature of the market model, the optimal consumption and the optimal investment were derived from our wealth process. Risky asset price () obeys a geometric Brownian motion. The method used is the dynamic programming principle which is used to derive the Hamilton-Jacobi-Bellman equation (HJB) which is a second-order non-linear differential equation. In addition, we analyzed the optimal consumption of an investor for 10years and our result shows that the optimal consumption of the investor is to consume a fraction of his wealth which also coincides with the wealth at the terminal. We also focused on analyzing the optimal bond/stock mix for a single stock. Our result shows that for a logarithmic investor, investing a large part of their wealth on stock tends to yield higher returns. An illustrative example is given.
TABLE OF CONTENTS
Title Page---------
Approval Page--------
Declaration--------
Dedication---------
Acknowledgement-------
Abstract---------
Table of Contents-------
CHAPTER ONE – INTRODUCTION
1.1Background of the Study-----
1.2Statement of the Problem----
1.3Objectives of the Study------
1.4Research Questions------
1.5Research Hypothesis------
1.6Significance of the Study-----
1.7Scope of the Study------
1.8 Limitations of the Study - - - - -
1.9Definition of Terms------
CHAPTER TWO – REVIEW OF RELATED LITERATURE
2.1Introduction-------
2.2Theoretical Framework-----
2.3Conceptual Framework-----
2.4 Empirical Review - - - - - -
CHAPTER THREE – RESEARCH METHODOLOGY
3.1Introduction-------
3.2Research Design------
3.3Population of Study------
3.4Sample size and Sampling Techniques---
3.5Method of Data Collection-----
3.6 Research Instrument
3.7Validity of the Instrument-----
3.8Reliability of the Instrument----
3.9Sampling Method------
CHAPTER FOUR – DATA PRESENTATION AND ANALYSIS
4.1Introduction-------
4.2Data Presentation and Analysis----
4.3Testing Hypothesis------
CHAPTER FIVE – SUMMARY, CONCLUSION AND RECOMMENDATION
5.1Summary--------
5.2Conclusion--------
5.3Recommendations------
References --------
Appendix - - - - - - - -
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