The scaling properties of the time series of asset prices and trading volumes of stock markets are analysed. It is shown that similar to the asset prices, the trading volume data obey multi-scaling length-distribution of low-variability periods. In the case of asset prices, such scaling...

Based on empirical financial time-series, we show that the "silence-breaking" probability follows a super-universal power law: the probability of observing a large movement is inversely proportional to the length of the on-going low-variability period. Such a scaling law has been previously...

The scaling properties of the time series of asset prices and trading volumes of stock markets are analysed. It is shown that similarly to the asset prices, the trading volume data obey multi-scaling length-distribution of low-variability periods. In the case of asset prices, such scaling...

The question of optimal portfolio is addressed. The conventional Markowitz portfolio optimisation is discussed and the shortcomings due to non-Gaussian security returns are outlined. A method is proposed to minimise the likelihood of extreme non-Gaussian drawdowns of the portfolio value. The...

Properties of low-variability periods in the time series are analysed. The theoretical approach is used to show the relationship between the multi-scaling of low-variability periods and multi-affinity of the time series. It is shown that this technically simple method is capable of revealing...

The optimal planning of Monte-Carlo simulations is studied. It is assumed that (i) the aim of the simulations is to calculate the value of a certain parameter of a model function as accurately as possible; (ii) the simulations are performed at different values of the control parameter L; (iii)...

In this chapter the complex systems are discussed in the context of economic and business policy and decision making. It will be showed and motivated that social systems are typically chaotic, non-linear and/or non-equilibrium and therefore complex systems. It is discussed that the rapid change...

This paper is aimed to explain the choice of instrument mix for EUR-based long-term equity investors, like pension funds, in the Eastern Europe. It is assumed that investments into local securities are the investorsí preferred choice. Markowitz mean-variance optimization was used for...