The basic problem in finance theory is the selection of an appropriate mix of assets in a portfolio in order to maximize portfolio expected return and subsequently to minimize portfolio risk. Another approach takes into account portfolio performance expressed by various measurement techniques e.g. Sharpe ratio, Treynor ratio, Jensen's alpha, Information ratio, Sortino ratio, Omega function and Sharpe Omega ratio that are focused on determine the allocation of the available resources in the selected group of assets. This paper presents the alternative approach computing the weights of assets in portfolio assets based on the nonlinear measure techniques: Sortino ratio and Omega function. The proposed alternative includes principle of differential evolution from the group of evolutionary techniques. The experiments are set up on assets included in Dow Jones Industrial Average. Presented original approach enables using also other evolutionary algorithms in the area of portfolio selection based on different measurement techniques.
The task of the traveling salesman, which is to find the shortest or least costly circular route, is one of the most common optimization problems that need to be solved in various fields of practice. The article analyzes and demonstrates various methods for solving this problem using a specific example: heuristic (the nearest neighbor method, the most profitable neighbor method), metaheuristic (evolutionary algorithm), methods of mathematical programming. In addition to classic exact methods (which are difficult to use for large-scale tasks based on existing software) and heuristic methods, the article suggests using the innovative features of the commercially available MS Excel software using a meta-heuristic base. To find the optimal solution using exact methods, the Excel (Solver) software package was used, as well as the specialized GAMS software package. Comparison of different approaches to solving the traveling salesman problem using a practical example showed that the use of traditional heuristic approaches (the nearest neighbor method or the most profitable neighbor method) is not difficult from a computational point of view, but does not provide solutions that would be acceptable in modern conditions. The use of MS Excel for solving the problem using the methods of mathematical programming and metaheuristics enabled us to obtain an optimal solution, which led to the conclusion that modern tools are an appropriate addition to solving the traveling salesman problem while maintaining the quality of the solution.
Paper presents alternative solution seeking approach for portfolio selection problem with Omega function performance measure which allows determining capital allocation over the number of assets. Omega function computability is diffi-cult due to substandard structures and therefore the use of standard techniques seems to be relatively complicated. Dif-ferential evolution from the group of evolutionary algorithms was selected as an alternative computing procedure. Al-ternative approach is analyzed on the Down Jones Industrial Index data. Presented approach enables to determine good real-time solution and the quality of results is comparable with results obtained by professional software
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