Research on the Cumulative Effect of Financial Innovation by Chaos Model Han Guo-wen Economics and Management School, Wuhan university, P.R. China, 430072 Department of Economics, Bar-Ilan University. Israel, 52900 Warren Young Department of Economics, Bar-Ilan University. Israel, 52900 ABSTRACT Based on an understanding and analysis of the complexity of a financial system and the chaotic features of its evolution, we focus upon how chaotic rules impact on financial innovation in the perspective of chaotic economic theory. A chaotic model of the cumulative effect of financial innovation is set up to study the factors affecting the cumulative effect of financial innovation. These include the impetus for innovation within the financial system itself, the pulling force of economic growth, regulation， and the factors that also slow down financial evolution. All of these influences are dictated by chaotic rules. Our approach should provide both deeper understanding and a wider basis for a regulatory authority to apply control in financial innovation. Keywords: Financial innovation, Cumulative effect, Chaos model 1. INTRODUCTION Financial innovation plays a vital role in reducing transaction costs and improving the efficiency of finance and resource-distribution, contributing a great deal to economic growth. Furthermore, in the evolution of financial systems, financial innovation not only reforms the traditional function mechanisms and improves the speed and efficiency of change; it also exerts profound influences on the supervision and management of the overall financial system. Financial development is at the core of economic growth. Needless to say without high-speed financial development, rapid economic growth rates will not be attainable and economic modernization will be impossible (Beck et al., 2000). For the financial system to play such a key role, the most important factor is its ability to accommodate financial innovation, including the introduction of new financial instruments and markets, new decision-making processes with management, new organization, as well as new institutions. In the Harrod-Domar growth model for example, the effect of financial innovation is reflected by its impact on economic growth. This is seen by its savings ratio, savings-investment transformation ratio, marginal investment efficiency and other factors; in the Ramsey growth model, financial innovation promotes economic growth by enhancing consumer substitution elasticity, reducing the average discount rate, as well as the rate of labor saving(Harrod,1939; Domar,1946). In the endogenous growth model, in addition to changing the substitution elasticity and discount rate, the path of economic growth may also be optimized by improving investment efficiency. Besides these functions, financial innovation can also deepen financial changes in the financial structure, and also speed up the flow of production factors, and stimulate capital accumulation. Financial innovation may result in some negative effects too, increasing the difficulty in implementing financial regulation and monetary policies, and even engendering financial crisis. Financial innovations function in various and complex ways. As a result, the appearance of one innovation after another continuously changes the equilibrium positions of the economic and financial markets, causing fluctuation. Previous research has indicated that such fluctuation is complex and irregular, and shows a lack of perfect periodicity. This kind of irregularity is called chaos. A great deal of literature focuses on financial innovation, but its cumulative effect has been overlooked. Our contribution is to examine the evolutionary characteristics of financial innovation, so we borrow the chaotic model to describe its complexity. 2. THE COMPLEXITY OF A FINANCIAL SYSTEM AND THE CHAOTIC FEATURE OF ITS EVOLUTION Chaos refers to indefinite or unpredictable phenomenon, like randomness appearing in the definite macroscopic nonlinear system. It appears to be out of order, but in fact is in some kind of order. It is characterized as both definite and indefinite, both regular and irregular, and both ordered and disordered. Seen from a mathematical perspective, this randomness comes from the systemic equation, which is not stochastic at all, but a difference or differential equation. Chaos has been identified in hydrodynamic turbulence, lasers, electrical circuits, chemical reactions, disease epidemics, biological reactions, and climatic change. Financial researchers have attempted to establish whether the apparently random nature of asset prices and economic time series could also be explained by the presence of chaotic behaviour. Substantial empirical evidence of nonlinear structure in a wide range of financial system has been presented in the past decades(see Brock, Dechert, and Scheinkman, 1998; Brock, 1997; Gallas, 1996; Chen . 2001 ;etc). Chaos 1-4244-0885-7/07/$20.00 ©2007 IEEE.