On The Closed Form Strategies of an Investor under the CEV and CIR Processes

  • Edikan E. Akpanibah Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria.
  • Bright O. Osu Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria.
  • Everestus O. Eze Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria.
  • Chidi U. Okonkwo Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria.
  • Ben I. Oruh Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria.
  • Udeme O. Ini Department of Mathematics and Computer Science, Niger Delta University, Bayelsa, Nigeria.
DOI: https://doi.org/10.52968/28306828
Keywords: Asymptotic technique, CEV process, Cox-Ingersoll-Ross process, Exponential utility, Optimal investment plan, Power transformation

Abstract

In this paper, the explicit solutions of the optimal investment plans of an investor with exponential utility function exhibiting constant absolute risk aversion (CARA) under constant elasticity of variance (CEV) and stochastic interest rate is studied. A portfolio comprising of a risk-free asset modelled by the Cox-Ingersoll-Ross (CIR) process and two risky assets modelled by the CEV process is considered, where the instantaneous volatilities of the two risky assets form a 2 × 2 matrix n = {n p,q } 2×2 such that nn T is positive definite. Using the power transformation and change of variable approach with asymptotic expansion technique, explicit solutions of the optimal investment plans are found. Moreover, numerical simulations are used to study the effects of the interest rate, elasticity parameter, correlation coefficient and the risk averse coefficient on the optimal investment plans.

Published
2021-10-23
How to Cite
Akpanibah, E. E., Osu, B. O., Eze, E. O., Okonkwo, C. U., Oruh, B. I., & Ini, U. O. (2021). On The Closed Form Strategies of an Investor under the CEV and CIR Processes. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 7(1), 87 - 107. https://doi.org/10.52968/28306828
Issue
Vol 7 No 1 (2021)
Section
Articles

This is an Open Access article distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, adaptation, and reproduction in any medium, provided that the original work is properly cited.