## Mathematical Modelling of Investment Strategies for Commercial Banks under Heston’s Volatility Model

Published: 2022-05-27

Page: 363-375

Department of Mathematics and Statistics, Federal University Otuoke, Bayelsa, Nigeria.

E. E. Akpanibah *

Department of Mathematics and Statistics, Federal University Otuoke, Bayelsa, Nigeria.

*Author to whom correspondence should be addressed.

### Abstract

This paper studies investment in commercial banks considering the present economic situations in the world orchestrated by corona virus pandemic (Covid-19) and other factors affecting the financial market. Based on this, there is need to develop an efficient investment strategy that takes into consideration the volatility of the stock market price. As a result of this, the optimal distribution strategies for a commercial bank with investment in three assets namely risk free asset (fixed deposit) and two risky assets (stock and loan) is studied where the price process of the stock market price is modelled by the Heston’s volatility model and the price process of the loan is modelled by geometric Brownian motion. The maximum principle and Ito’s lemma are use to establish an optimization problem from the Hamilton Jacobi Bellman (HJB) equation which is a non-linear partial differential equation (PDE). The power transformation and change of variable technique is used to solve for the explicit solutions of the optimal distribution strategies under exponential utility function. Furthermore, some numerical simulations are presented to study the effects of some sensitive parameters of the optimal distribution strategies with observations that the behaviour of the correlation coefficient, risk averse coefficient, appreciation rate of the risky assets, initial wealth of the bank, instantaneous volatilities and risk free interest rate plays vital role in the determination of the proportion to be invested in any of the three asset by the bank’s investment team.

Keywords: Optimal distribution strategies, commercial bank, exponential utility, Heston volatility, Hamilton Jacobi Bellman equation

#### How to Cite

Amadi, U. C., & Akpanibah, E. E. (2022). Mathematical Modelling of Investment Strategies for Commercial Banks under Heston’s Volatility Model. Asian Journal of Pure and Applied Mathematics, 4(1), 363–375. Retrieved from https://globalpresshub.com/index.php/AJPAM/article/view/1608

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