带风险指数的金融均衡的存在性定理及其结构特征(下)

THE THEOREM OF EXISTENCE AND THE CHARACTERISTICS OF STRUCTURE ABOUT THE FINANCIAL EQUILIBRIUM WITH RISK FACTORS(Ⅱ)

本文主要论证了在不完全市场条件下带风险指数的金融均衡的存在性，并揭示其均衡结构的特征．本文中建立的模型是一、二期货币投入产出金融经济且具有可微的资产结构，这一模型包括了许多具有特殊资产结构的均衡模型，如实资产结构、虚资产结构、恒秩资产结构的均衡模型．因此本文的这一模型具有广泛的应用前景和实用价值．接着给出了本文的金融均衡的存在性定理，再借助微分拓扑给出它的证明过程，这一证明过程较之以前证明均衡存在性的经典方法（如Duffie，D＆W．Shfer（1985）的方法）要简便得多．同时也应注意到本文的这一结论既适用于资产市场下会随机风险因素的情形，也适用于商品空间为无限维的情形，除此之外，还给出了怎样判别资产结构是否属于T类的判别法，为检验均衡存在性提供了更为便利的途径．最后，本文论证了在金融市场里，尽管由于稀缺性的存在，从而导致均衡分配的多样化，然而均衡分配集却形成了一光滑子流，但该流形的维数与稀缺性有关．换句话说，尽管市场是不完全的，但均市分配不确定性的反却是可比的．如此使得人们对均衡资产结构的认识更进一步．

This paper mainly argues the existence of the financial equilibrium with risk factors in incomplete market and studies its characteristic of structure at equilibrium point. Theestablished model in our paper,which is a two-peniod-money input-output financial economywith differentiable asset structure,contains many equilibrium models of having especial assetstructure, for instance, real asset structure, nominal asset structure, fixed rank asset structure. Hence,out model has broad applied prospects and applied values.Followingly, we present the existence theorem of financial equilibrium. By aid of differentiable topology we can finish its argument. The process of proof is much simpler than the former classical ones,for example,see Duffie,D and W. Shafer (1985)Meanwhile it should alsobe attended that our results are suitable for both asset modles with stochastic risk factors andmodels with infinite dimension commodity space. Besides there , we additionly indicate ametheod which can tell us how to distinct a asset structure belonging whether to class T ornot. At the same time ,the paper also provids a more convenient method for clecking equilibrium existence.Finally,we have argued that in financial market,becanse of the existence of deficiency,it willresult to the variousness of equilibrium allocation,but the set of equilibrium allocations willcontains a smooth submanifold. Its dimension is relate to the deficiency. In other words,though market is incomplete,the uncertain degree of equilibrium allocations is comparable.So it makes that man's recognition of equilibrium asset structure go a new further step forward.