Abstract
This paper is aim at maximizing the expected utility of an investor’s terminal wealth; to achieve this, we study the optimal portfolio strategy for an investor with logarithm utility function under constant elasticity of variance (CEV) model in the presence of stochastic interest rate. A portfolio comprising of one risk free asset and one risky asset is considered where the risk free interest rate follows the Cox- Ingersoll-Ross (CIR) model and the risky asset is modelled by CEV. Using power transformation, change of Variable and asymptotic expansion technique, an explicit solution of the optimal portfolio strategy and the Value function is obtained. Furthermore, numerical simulations are presented to study the effect of some parameters on the optimal portfolio strategy under stochastic interest rate.
Highlights
In the study of optimal portfolio strategy in a financial market, volatility plays a vital role in influencing the behaviour of the risky assets due to its fluctuating nature as a result of different information available in the financial market
For an investor to make relatively right choice when investing in risky assets, there is need to consider stochastic volatility models and not constant volatility in order to understand the fluctuating na
The graph shows that the investor will invest more in marketable security and gradually increases investment in treasury security to balance with the marketable security and as expiry date draws closer; there is a continuous decrease in investment in risky asset and a continuous increase in that of risk free asset
Summary
In the study of optimal portfolio strategy in a financial market, volatility plays a vital role in influencing the behaviour of the risky assets due to its fluctuating nature as a result of different information available in the financial market. They pointed out that one of the main reasons why other authors could not combined CEV model and stochastic interest in finding the optimal portfolio strategies was in the difficulty to find a closed form solution of the optimal portfolio strategies analytically They pointed out that in financial market, interest rate is not constant rather a fluctuating processes and that the interest rate volatility presents another source of risks in financial market; In other words, when this risk is not taken into consideration, we are undermining the risk generated by this interest rate which is crucial in affecting the prices of various assets available in financial market. The main difference between our work and that of [17] is that we consider an investor with logarithm utility instead of exponential utility and apply power transformation method and change of variable method instead of Legendre transformation method
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
