A financial market comprising of a certain number of distinct companies is considered, and the following statement is proved: either a specific agent will surely beat the whole market unconditionally in the long run, or (and this "or" is not exclusive) all the capital of the market will accumulate in one company. Thus, absence of any "free unbounded lunches relative to the total capital" opportunities lead to the most dramatic failure of diversity in the market: one company takes over all other until the end of time. In order to prove this, we introduce the notion of perfectly balanced markets, which is an equilibrium state in which the relative capitalization of each company is a martingale under the physical probability. Then, the weaker notion of balanced markets is discussed where the martingale property of the relative capitalizations holds only approximately, we show how these concepts relate to growth-optimality and efficiency of the market, as well as how we can infer a shadow interest rate that is implied in the economy in the absence of a bank.
We prove that in smooth Markovian continuous-time economies with potentially complete asset markets, Radner equilibria with endogenously complete markets exist.
This paper introduces a new financial metric for the art market. The metric is based on the price per unit of area and is applicable to two-dimensional art objects such as paintings.
A new chaotic financial system is proposed by considering ethics involvement in a four-dimensional financial system with market confidence. A five-dimensional conformable derivative financial system is presented by introducing conformable fractional calculus to the integer-order system. A discretization scheme is proposed to calculate numerical solutions of conformable derivative systems. The scheme is illustrated by testing hyperchaos for the system.
Using a modified damped harmonic oscillator model equivalent to a model of market dynamics with price expectations, we analyze the reaction of financial markets to shocks. In order to do this, we gather data from indices of a variety of financial markets for the 1987 Black Monday, the Russian crisis of 1998, the crash after September 11th (2001), and the recent downturn of markets due to the subprime mortgage crisis in the USA (2008). Analyzing those data we were able to establish the amount by which each market felt the shocks, a dampening factor which expresses the capacity of a market of ab…
We investigate whether fractal markets hypothesis and its focus on liquidity and invest- ment horizons give reasonable predictions about dynamics of the financial markets during the turbulences such as the Global Financial Crisis of late 2000s. Compared to the mainstream efficient markets hypothesis, fractal markets hypothesis considers financial markets as com- plex systems consisting of many heterogenous agents, which are distinguishable mainly with respect to their investment horizon. In the paper, several novel measures of trading activity at different investment horizons are introduced th…
Designing a financial market that works well is very important for developing and maintaining an advanced economy, but is not easy because changing detailed rules, even ones that seem trivial, sometimes causes unexpected large impacts and side effects. A computer simulation using an agent-based model can directly treat and clearly explain such complex systems where micro processes and macro phenomena interact. Many effective agent-based models investigating human behavior have already been developed. Recently, an artificial market model, which is an agent-based model for a financial market, ha…
We contrast Arbitrage Pricing Theory (APT), the theoretical basis for the development of financial instruments, with a dynamical picture of an interacting market, in a simple setting. The proliferation of financial instruments apparently provides more means for risk diversification, making the market more efficient and complete. In the simple market of interacting traders discussed here, the proliferation of financial instruments erodes systemic stability and it drives the market to a critical state characterized by large susceptibility, strong fluctuations and enhanced correlations among risk…
The purpose of this article is to propose a new "theory," the Strategic Analysis of Financial Markets (SAFM) theory, that explains the operation of financial markets using the analytical perspective of an enlightened gambler. The gambler understands that all opportunities for superior performance arise from suboptimal decisions by humans, but understands also that knowledge of human decision making alone is not enough to understand market behavior --- one must still model how those decisions lead to market prices. Thus are there three parts to the model: gambling theory, human decision making,…
I study the limit of a large random economy, where a set of consumers invests in financial instruments engineered by banks, in order to optimize their future consumption. This exercise shows that, even in the ideal case of perfect competition, where full information is available to all market participants, the equilibrium develops a marked vulnerability (or susceptibility) to market imperfections, as markets approach completeness and transaction costs vanish. The decrease in transaction costs arises because financial institutions exploit trading instruments to hedge other instruments. This ent…
Prediction problems in finance go beyond estimating the unknown parameters of a model (e.g. of expected returns). This is because such a model would have to include parameters governing the market participants' propensity to change their opinions on the validity of that model. This leads to a well--known circular situation characteristic of financial markets, where participants collectively create the future they wish to estimate. In this paper, we introduce a framework for organizing multiple expectation models and study the conditions under which they are adopted by a majority of market part…
With the random matrix theory, we study the spatial structure of the Chinese stock market, American stock market and global market indices. After taking into account the signs of the components in the eigenvectors of the cross-correlation matrix, we detect the subsector structure of the financial systems. The positive and negative subsectors are anti-correlated each other in the corresponding eigenmode. The subsector structure is strong in the Chinese stock market, while somewhat weaker in the American stock market and global market indices. Characteristics of the subsector structures in diffe…
This paper contributes to the literature on international stock market comovements and contagion. The novelty of our approach lies in application of wavelet tools to high-frequency financial market data, which allows us to understand the relationship between stock markets in a time-frequency domain. While major part of economic time series analysis is done in time or frequency domain separately, wavelet analysis combines these two fundamental approaches. Wavelet techniques uncover interesting dynamics of correlations between the Central and Eastern European (CEE) stock markets and the German D…
Financial markets are systems with the complex behavior, that can be hardly analyzed by means of linear methods. Recurrence Quantification Analysis (RQA) is a nonlinear methodology, which is able to work with the nonstationary and short data series. Thus, we apply RQA for the studying of the critical events on financial markets. For the present research, stock crashes of DJI 1929; DJI, NYSE and S&P500 1987; NASDAQ 2000; HSI 1994, 1997 and Spanish 1992, Portuguese 1992, British 1992, German 1992, Italian 1992, Mexican 1994, Brazilian 1999, Indonesian 1997, Thai 1997, Malaysian 1997, Philippine …
Financial market is an example of complex system, which is characterized by a highly intricate organization and the emergence of collective behavior. In this paper, we quantify this emergent dynamics in the financial market by using concepts of network synchronization. We consider networks constructed by the correlation matrix of asset returns and study the time evolution of the phase coherence among stock prices. It is verified that during financial crisis a synchronous state emerges in the system, defining the market's direction. Furthermore, the paper proposes a statistical regression model…
We introduce tools to capture the dynamics of three different pathways, in which the synchronization of human decision-making could lead to turbulent periods and contagion phenomena in financial markets. The first pathway is caused when stock market indices, seen as a set of coupled integrate-and-fire oscillators, synchronize in frequency. The integrate-and-fire dynamics happens due to change blindness, a trait in human decision-making where people have the tendency to ignore small changes, but take action when a large change happens. The second pathway happens due to feedback mechanisms betwe…
Nowadays, when crashes and crises are rather frequent events, an effective monitoring system for the international financial market is needed. Modern nonlinear methods, such as Recurrence Quantification Analysis (RQA), demonstrate the ability to reveal the regularities of the system behavior. Thus, they can be useful for the analysis of the market state in real time. In present paper we did an effort to apply the RQA for the purpose of economic time series monitoring. 12 stock indexes, 6 currency pairs and 4 commodities were taken for the study.
