以往財務理論在討論財務市場行為時，均是在完全市場( e market)的假

設上做分析。但是從現實的角度來看，由於時間 (time)與不確定(uncertainty)

等因素，導致市場往往是不完全的(incomplete)；亦即資產或證券的數目往往小

於未來各種可能發生的不確定狀態的數目。當各種不同狀態事件發生時,如果沒有足夠的

資產或證券工具來涵括(span)所有投資人所欲達成的跨時所得移轉，則有某些風

險因子不能以既有的財務工具來複製，此時投資人將無法完全地規避該項風險。

本文的分析方法屬於微分拓樸數學工具的應用。從基本可微分流行(differentiable

manifold) 性質，我們可得到整體性的觀點，優於以往在歐氏空間，Hilbert 空

間等拓樸空間只考慮在局部的性質.首先由最基本平滑流形(smooth manifo-[念

切入，介紹平滑流形與歐氏空間的關係。再由市場均衡的定義找出均衡流形(

equilibrium manifold)。結合Debreu(1970)與Balasko(1976,1988) 建立的正

規經濟，探討其性質.加入財務市場時，透過正規經濟的理論，證明不完全財物

市場均衡generic 存在性。最後，利用不完全財務市場均衡generic的存在性，證明單

一商品及多商品的資本資產定價(CAPM)；並且建立一以消費為基礎的資本資

產定價模式。

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