Research Of Financial Supernetwork Based On Variational Inqualities

With the Financial crisis occurring again and again, people begin to be pay attention to financial problems, explore the law of it, try to find out the research approaches and the research ways. These can make financial industry develop orderly and healthy. At present, there are many results researching on the financial aspect, some research methods and conclusions have been mature. But most of the researchers are standing in a particular individual's view to premeditate some target (for example:profit maximization), who considered the whole optimization problem is seldom. As a research method, supernetwork theory's research objects are more complex network (Multi-object, multi-attribute, multi-objects, etc.). It can convert practical problems into mathematical models, consider and solve problems as a whole to achieve the optimization of the whole network.Therefore, this paper combines the supernetwork theory with the financial network, presents a financial supernetwork model with several influencing factors. It consists of 3 tiers:agents with sources of funds, intermediaries and consumers at the demand market. Every decision-maker wants to optimize their objective functions and they face with two criterias (maximize profit and minimum risk). In the model, the decision-makers compete within a tier and cooperate between tiers to optimize the whole financial supernetwork. In particular, we add three influencing factors which have an impact on decision making to every decision-maker and the whole financial supernetwork. On this base, the optimality conditions for the agents with sources of funds, intermediaries and consumers at the demand market are established respectively using the variational inequalities. Then we describe the optimization situation for the financial supernetwork model, prove the existence and uniqueness of the optimal condition, depict and prove the algorithm combining with the model. Finally, an example is provided to illustrate the rationality of the supernetwork model.