关键词: Incomplete financial market, bounded linear operator, metric generalized inverse, single-value selection, Moore-Penrose generalized inverse

Abstract: This article continues to study the research suggestions in depth made by M.Z. Nashed and G.F. Votruba in the journal "Bull. Amer. Math. Soc." in 1974. Concerned with the pricing of non-reachable "contingent claims" in an incomplete financial market, when constructing a specific bounded linear operator $A: l_1^n\rightarrow l_2$ from a non-reflexive Banach space $l_1^n$ to a Hilbert space $l_2$, the problem of non-reachable "contingent claims" pricing is reduced to researching the (single-valued) selection of the (set-valued) metric generalized inverse $A^\partial$ of the operator $A$. In this paper, by using the Banach space structure theory and the generalized inverse method of operators, we obtain a bounded linear single-valued selection $A^\sigma=A^+$ of $A^\partial$.

Key words: Incomplete financial market, bounded linear operator, metric generalized inverse, single-value selection, Moore-Penrose generalized inverse