Department of Mathematics and Informatics

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    On Steady Dividend Payment under Functional Mean Reversion Speed
    (Journal of Mathematical Finance, 2016-08) Mtunya, Adeline Peter; Ngare, Philip; Nkansah-Gyekye, Yaw
    We study how firms’ management can ensure steady dividend growth and payout to the shareholders in an emerging market. We create the dividend equalization reserve account whereby during high profit some amount of money is kept in order to top up dividends during deficiency. We use a mean reversion stochastic differential equation with a functional mean reversion speed to find the optimal dividend policy with optimal dividend equalization reserve. One of our results indicates that, it is optimal to pay high dividends when we have high mean levels. Also, we realized that a higher level of volatility which implies more dividend can be paid. And high dividend can also be paid as the interest rate rises but this is more significant when the firm makes profits above average. Lastly, we compared the buffer approach to a situation where hedging was not applied and found that the buffering approach is more suitable because it gives shareholders steady dividend payments.
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    STEADY DIVIDEND PAYMENT AND INVESTMENT FINANCING STRATEGY: A FUNCTIONAL MEAN REVERSION SPEED APPROACH
    (Journal of Mathematical and Computational Science, 2017) Mtunya, Adeline Peter; Ngare, Philip; Nkansah-Gyekye, Yaw
    We study how corporate firms’ management can satisfy the shareholders by steady and growing dividend payouts while financing investment growth from the profit. We set the percentage of the profit which is optimal for steady dividends and the rest to be allocated for investment and dividend buffer account. A mean reversion stochastic differential equation with investment function in the drift term has been used to find the optimal dividend and retainment levels. One of the findings shows that for each level of profit there exists a percentage which is optimal for paying steady dividends while financing investment growth. Also we find that having low interest rates is favourable for the strategy of paying steady dividend with investment growth. Moreover, we compared the proposed strategy with a situation of steady dividend without investment and found that the strategy with investment is more appropriate as it gives more values to the shareholders. In addition we find that the exponential and linear responses of the investment function on investment amount give out the same results. Companies in developing economies should consider steady and growing dividends as they expand their investments, while policies of such economies should enforce low interest rates and influence companies to pay dividends.
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    Optimal Investment Strategy under Stochastic Interest Rates
    (Journal of Mathematical Finance, 2017-05-19) Mtunya, Adeline Peter; Ngare, Philip; Nkansah-Gyekye, Yaw
    We study how firms’ management can make effective investment decision under the influence of random interest rates. We define the threshold interest rate value below which investment can be effectively done and above which investment is not optimal. We use a stochastic differential equation with alternating drift to find the optimal investment policy under stochastic interest rate. One of our results indicated that, the optimal condition for investment expansion is when the interest rate is low and the profit level is high. Also, there exists the threshold interest rate value which forms the basis for investment decision of a company. Moreover, we revealed that it is not optimal for the managers to plan for firm’s business expansion when is already making extremely high profits. At the end we were able to confirm that business is generally more stable when the interest rates are lower than those when they are high. Since firms in emerging economies suffer most from interest rate fluctuations, they need more effective investment strategies. Monetary policy makers of such economies need to ensure low interest rates in order to promote firms’ investment and therefore boost the general economy.