GENERALISED OPTIMAL STOPPING STRATEGIES WITH APPLICATIONS TO FINANCE

In this paper we examine the problem of determining the best time to sell an asset, where the stock price is modelled by a hybrid process. In this paper hybrid variable is a mathematical concept that is used to describe a situation in which randomness and fuzziness simultaneously appear in a system or phenomenon. Based on this concept, a hybrid stopping time problem is formulated and investigated. A verification theorem is derived and proved. We illustrate the application of the verification theorem through a practical example in mathematics of finance. A power function with exponent , is used as the utility function in the example. This study is extending the model from Oksendal [12] by including the fuzzy component since market value of assets is usually described using vague human language. The theory of hybrid variables provides a more realistic description of the evolution of price processes of financial assets. Keywords: Randomness, fuzziness, Fuzzy variable, fuzzy process, hybrid variable, hybrid process, stopping time

Optimal stochastic control and risk minimisation in Insurance

The thesis examines a generalised problem of optimal control of a firm through reinsurance, dividend policy and convex risk minimisation in the presence of market friction. The major mathematical tool applied is the theory of stochastic control for jump-diffusions. In the absence of intervention the financial reserves of the firm are assumed to evolve according to a stochastic differential equation with a jump component. In the second and third chapters, the objective is to derive reinsurance and dividend policies that maximize the expected total discounted value of a spectrally negative process in incomplete markets. The assumption is that transaction costs are incurred whenever dividends are paid out. Several verification theorems are derived and proved for combined singular and impulse control. The verification theorems are new results which provide a federative approach to the analysis of control problems involving transaction costs in finance and insurance. Two methodologies are examined for risk minimisation. First, we investigate risk minimisation using zero-sum stochastic differential game theory in the presence of transaction costs. Our major contribution in this direction is that we have investigated, for the first time in the literature, a singular control problem for jump 7 diffusion stochastic differential games. Hamilton-Jacobi-Bellman-Isaacs variational inequalities (HJBIVI) are formulated and proved for the case of zero-sum stochastic differential games. The notion of HJBIVI is later on extended to the more general case of Nash equilibrium. Minimisation of risk is also studied using g-expectation. In this case a five step scheme is formulated. The scheme constitutes a mechanism for solving forward-backward stochastic differential equations. The solution provided by such a scheme minimises risk of terminal wealth of an insurance company. An existence and uniqueness theorem for the solution is provided. Several examples are discussed, throughout the thesis, to illustrate the theory.,NUF

Corporate Loan Recovery Rates under Downturn Conditions in a Developing Economy: Evidence from Zimbabwe

In this study, we design stepwise ordinary least squares regression models using various amalgamations of firm features, loan characteristics and macroeconomic variables to forecast workout recovery rates for defaulted bank loans for private non-financial corporates under downturn conditions in Zimbabwe. Our principal aim is to identify and interpret the determinants of recovery rates for private firm defaulted bank loans. For suitability and efficacy purposes, we adopt a unique real-life data set of defaulted bank loans for private non-financial firms pooled from a major anonymous Zimbabwean commercial bank. Our empirical results show that the firm size, the collateral value, the exposure at default, the earnings before interest and tax/total assets ratio, the length of the workout process, the total debt/total assets ratio, the ratio of (current assets–current liabilities)/total assets, the inflation rate, the interest rate and the real gross domestic product growth rate are the significant determinants of RRs for Zimbabwean private non-financial firm bank loans. We reveal that accounting information is useful in examining recovery rates for defaulted bank loans for private corporations under distressed financial and economic conditions. Moreover, we discover that the prediction results of recovery rate models are augmented by fusing firm features and loan characteristics with macroeconomic factors

An An empirical study on the factors influencing the performance of financial institutions in Zimbabwe

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