Based on our "finance-prediction-oriented" methodology which involves such elements as log-periodic self-similarity, the universal preferred scaling factor lambda=2, and allows a phenomenon of the "super-bubble" we analyze the 2009 world stock market (here represented by the SP500, Hang Seng and...

We study Atlas-type models of equity markets with local characteristics that depend on both name and rank, and in ways that induce a stable capital distribution. Ergodic properties and rankings of processes are examined with reference to the theory of reflected Brownian motions in polyhedral...

This article focuses on the mathematical problem of existence and uniqueness of BSDE with a random terminal time which is a general random variable but not a stopping time, as it has been usually the case in the previous literature of BSDE with random terminal time. The main motivation of this...

We investigate the probability distributions of the recurrence intervals $\tau$ between consecutive 1-min returns above a positive threshold $q0$ or below a negative threshold $q0$ of two indices and 20 individual stocks in China's stock market. The distributions of recurrence intervals for...

In this study we consider relations between companies in Poland taking into account common branches they belong to. It is clear that companies belonging to the same branch compete for similar customers, so the market induces correlations between them. On the other hand two branches can be...

Financial correlation matrices measure the unsystematic correlations between stocks. Such information is important for risk management. The correlation matrices are known to be ``noise dressed''. We develop a new and alternative method to estimate this noise. To this end, we simulate certain...

We study the long-term memory in diverse stock market indices and foreign exchange rates using the Detrended Fluctuation Analysis(DFA). For all daily and high-frequency market data studied, no significant long-term memory property is detected in the return series, while a strong long-term memory...

We investigate sets of financial non-redundant and nonsynchronously recorded time series. The sets are composed by a number of stock market indices located all over the world in five continents. By properly selecting the time horizon of returns and by using a reference currency we find a...

We analyze the time series of overnight returns for the bund and btp futures exchanged at LIFFE (London). The overnight returns of both assets are mapped onto a one-dimensional symbolic-dynamics random walk: The `bond walk'. During the considered period (October 1991 - January 1994) the...

Utility based methods provide a very general theoretically consistent approach to pricing and hedging of securities in incomplete financial markets. Solving problems in the utility based framework typically involves dynamic programming, which in practise can be difficult to implement. This...