CRITICAL ANALYSIS OF MANAGING INVESTMENT PORTFOLIO METHODS

The article discusses mathematical methods for managing a portfolio of securities. The classical approaches of G. Markowitz, J. Tobin, W. Sharp, P. Samuelson, F. Black, M. Scholes, R. Merton are considered. The features that complicate the practical application of classical methods are revealed. Alternative methods, such as the method of neural networks, the decision tree method, genetic algorithm, simulation modeling, methods of dynamic portfolio restructuring of investment portfolio management, are also considered. In all the considered methods, the features that characterize the positive and negative aspects of their practical application are highlighted. On the basis of the considered methods were proposed directions for finding a method that are best suited for managing an investment portfolio.

Portfolio Selection with Transaction Costs and Jump-Diffusion Asset Dynamics II: Economic Implications

We derive allocation rules under isoelastic utility for a mixed jump-diffusion process in a two-asset portfolio selection problem with finite horizon in the presence of proportional transaction costs; we allow cash dividends on the risky asset. The allocation shifts toward the riskless asset relative to diffusion in varying degrees depending on parameter values. It is sensitive to the proportion of the jump component to total volatility, but also to the expected amplitude for a given proportion. The shift becomes small when the relative risk aversion increases, but it becomes major when the solvency constraint is active in the presence of jumps. We derive utility losses and risk premia due to jumps under realistic parameter values, and show that even when the no transaction region is very similar between pure diffusion and the mixed process the latter corresponds to lower utility because of higher portfolio restructuring costs.