摘要
在非均衡市场套利机会存在性研究的基础上 ,定义了市场的可及性和完备性 ,再根据定义讨论市场的完备性 ,利用线性空间的相关知识得到判别市场完备性的一个充要条件。该条件认为 ,在m≥n的情况下 ,只要存在一个F(m)t 适应的矩阵价值过程σ-1(t,ω) ∈Rm×n,满足秩σ(t,ω) =m ,a .a .(t,ω) ,则市场 {X(t) }就是完备的。在同样的假设条件下 ,利用该定理得到了在m =n时判别市场完备性的一个更为简洁的结果 ,以及在市场完备性的条件下求取u(t,ω)的唯一表达式。
This article is based on the existence of an arbitrage about portfolio in an disequilibrium market, the mathematics definitions of a market's attainability and Completeness are given according to these definitions.The completeness of a market is discussed and a sufficient and necessary condition of a market's completeness with the knowledge of line space is gotten. With the condition, a market is complete if and only if there exists a F (m) t -adapted matrix value process σ -1 (t,ω)∈R m×n ,such that rank σ(t,ω)=m,a.a.(t,ω) .Under the condition, especially when m=n , resulted a furthermore condision outcome, in addition, under the condition of completeness, the only expression of u(t,ω) is gotten.
出处
《重庆大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2002年第5期136-139,共4页
Journal of Chongqing University
关键词
可及性
完备性
期权
attainability
completeness
option
