Mathematical Models Applicable in Business Investments

Abstract

The increasing reliance of finance and economics on mathematical models has made it necessary for managers, economists, and students to have some understanding of certain mathematical methods. However, the highly technical nature of many models often in applied in mathematics discourage managers and economists from using quantitative methods as tools in conceptualizing and solving business problems. The field of investment is vast due to the fact that, theoretically, there is an infinitely wide choice with respect to a given investment project. The dimensions of choice are geared towards product/service, market, technology, equipment, and scale of production, time phasing, and location. The task is identifying investment opportunities, which are promising and which merit further examination and appraisal. There is need to come up with relations to solve discounted value of streams of income that the firm will generate in the future. This dissertation investigates the application of mathematical modelling in investment mathematics to help solve investment problems such as a series of cash flows. The dissertation uses systems of first order differential equations to relate investments and capital. It further uses linear difference equations in modifying the compound amount formula to obtain a simpler model for a series of cash flows. In addition, the annuities are solved by linear difference equations in areas of depositing and borrowing. The models discussed in dissertation have great importance in the sense that they consider a series of cash flows. The results obtained will help in management practices towards economic growth.