In this paper we reconcile why it is possible that people in finance view conventional portfolio selection as a single criterion problem and people in multiple criteria optimization view it as a bi-criterion problem. We then show how, for more complex investors, the theory of mean-variance portfolio selection can be extended to include additional objectives such as dividends, liquidity, turnove...

Portfolio theory is a very powerful tool in the modern investment theory. It is helpful in estimating risk of an investor’s portfolio, arosen from lack of information, uncertainty and incomplete knowledge of reality, which forbids a perfect prediction of future price changes. Despite of many advantages this tool is not known and not widely used among investors on Warsaw Stock Exchange. The main...

The purpose of this paper is to suggest a new theory of portfolio selection which is based on evolutionary reasoning in simple repeated market situations. According to this new point of view the ultimate success of a portfolio strategy is measured by the wealth share the strategy is eventually able to conquer in an evolutionary process of market selection. We identify a simple portfolio strateg...

The purpose of this paper is to suggest a new theory of portfolio selection which is based on evolutionary reasoning in simple repeated market situations. According to this new point of view the ultimate success of a portfolio strategy is measured by the wealth share the strategy is eventually able to conquer in an evolutionary process of market selection. We identify a simple portfolio strateg...

This paper deals with a portfolio selection problem with independently estimated possibilistic return rates. Under such a circumstance, a distributive investment has been regarded as a good solution in the traditional portfolio theory. However, the conventional possibilistic approach yields a concentrated investment solution. Considering the reason why a distributive investment is advocated, a ...

Investors use different approaches to select optimal portfolio. so, Optimal investment choices according to return can be interpreted in different models. The traditional approach to allocate portfolio selection called a mean - variance explains. Another approach is Markov chain. Markov chain is a random process without memory. This means that the conditional probability distribution of the nex...

The Modern Portfolio Theory of Markowitz maximized portfolio expected return subject to holding total portfolio variance below a selected level. Digital Portfolio Theory is an extension of Modern Portfolio Theory, with the added dimension of memory. Digital Portfolio Theory decomposes the portfolio variance into independent components using the signal processing decomposition of variance. The r...