Optimal portfolio of an investor in a financial market

Abstract

An investor seeks to diversify assets and optimal portfolio, which provide the maximum expected returns at a given level of risk. Optimal portfolio problems of an investor with logarithmic utility have been studied. However, there is scarce information on other utility functions, such as power utility function, which captures the concept of diversification of portfolios. This study was therefore designed to consider the general expected utility of an investor in the financial market. Ito’s integral where extended by the lofty properties of forward integral to diversify the investor’s portfolio. A filtration was built and used as a set of information for the investor. A semimartingale was used to enlarge the investor’s information. Matlab Mathematical software was used to compute the investors varying rates of return.