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In this paper, a new differential equation, driven by aleatory and epistemic forms of uncertainty, is introduced and applied to describe the dynamics of a stock price process. This novel class of differential equations is called uncertain stochastic differential equations(USDES) with uncertain jumps. The existence and uniqueness theorem for this class of differential equations is proposed and proved. An appropriate version of the chain rule is derived and applied to solve some examples of USDES with uncertain jumps. The differential equation discussed is applied in an American call option pricing problem. In this problem, it is assumed that the evolution of the stock price is driven by a Brownian motion, the Liu canonical process and an uncertain renewal process. MATLAB is employed for implementing the derived option pricing model. Results show that option prices from the proposed call option pricing formula increase as the jump size increases. As compared to the proposed call option pricing formula, the Black-Scholes overprices options for a certain range of strike prices and under-prices the same options for another range of exercise prices when the jump size is zero.

The main aim of this study was to empirically assess the main microeconomic factors that affect a bank's performance. The objectives were to ascertain if there is a relationship between the performance variables with the microeconomic variables, determine those that are significant and their impact on the performance of banks in Zimbabwe. An econometric model was built from balanced panel data and the Arellano-Bond estimation procedure was employed. The empirical analysis was carried out on a sample of 17 banks that were operational in the years 2010 to 2017 in Zimbabwe. Return on Assets (ROA), Return on Equity (ROE) and Net Interest Margin (NIM) were used as the performance indicators in the analysis. The results indicate the main microeconomic factors to be those attributed to growth, credit risk, capitalisation, managerial efficiency, liquidity and diversification in the Zimbabwean financial institutions. Performance in these institutions is generally good as measured by positive persistent profits, that is, ROA, ROE and NIM. These returns reflect the extent to which these institutions are resilient to the economic crisis.