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.

Ebola virus (EBOV) infection is a hemorrhagic and hazardous disease, which is among the most shocking threats to human health causing a large number of deaths. Currently, there are no approved curative therapies for the disease. In this study, a mathematical model for in-vivo Ebola virus transmission dynamics was analyzed. The analysis of the model mainly focused on the sensitivity of basic reproductive number,  pertaining to the model parameters. Particularly, the sensitivity indices of all parameters of  were computed by using the forward normalized sensitivity index method. The results showed that a slight change in the infection rate immensely influences  while the same change in the production rate of the virus has the least impact on . Thus, , being a determining factor  of the disease progression, deliberate control measures targeting the infection rate, the most positively sensitive parameter, are required. This implies that reducing infection rate will redirect the disease to extinction. Keywords: Ebola virus infection, immune response, sensitivity index, mathematical model.

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.

No abstract