In this note, we give a characterization of the minimal martingale measure for a general discrete-time incomplete financial market. Then we concretely work out the minimal martingale measure for a specific discrete-ti...In this note, we give a characterization of the minimal martingale measure for a general discrete-time incomplete financial market. Then we concretely work out the minimal martingale measure for a specific discrete-time market model in which the assets' returns in different times are independent.展开更多
This paper analyzes the aritrage free security markets and the general equilibrium existence problem for a stochastic economy with incomplete financial markets. Information structure is given by an event tree. This pa...This paper analyzes the aritrage free security markets and the general equilibrium existence problem for a stochastic economy with incomplete financial markets. Information structure is given by an event tree. This paper restricts attention to purely financial securities. It is assume that trading takes place in the sequence of spot markets and futures markets for securities payable in units of account. Unlimited short selling in securities is allowed. Financial markets may be incomplete: some consumption streams may be impossible to obtain by any trading strategy. Securities may be individually precluded from trade at arbitrary states and dates. The security price process is arbitrage free the dividend process if and only if there exists a stochstic state price (present value) process: the present value of the security prices at every vertex is the present value of their dividend and capital values over the set of immediate successors; the current value of each security at every vertex is the present value of its future dividend stream over all succeeding vertices. The existence of such an equilibrium is proved under the following condition: continuous, weakly convex, strictly monotone and complete preferences, strictly positive endowments and dividends processes.展开更多
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 cla...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)→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■ 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^(σ)=A+of A■.展开更多
文摘In this note, we give a characterization of the minimal martingale measure for a general discrete-time incomplete financial market. Then we concretely work out the minimal martingale measure for a specific discrete-time market model in which the assets' returns in different times are independent.
文摘This paper analyzes the aritrage free security markets and the general equilibrium existence problem for a stochastic economy with incomplete financial markets. Information structure is given by an event tree. This paper restricts attention to purely financial securities. It is assume that trading takes place in the sequence of spot markets and futures markets for securities payable in units of account. Unlimited short selling in securities is allowed. Financial markets may be incomplete: some consumption streams may be impossible to obtain by any trading strategy. Securities may be individually precluded from trade at arbitrary states and dates. The security price process is arbitrage free the dividend process if and only if there exists a stochstic state price (present value) process: the present value of the security prices at every vertex is the present value of their dividend and capital values over the set of immediate successors; the current value of each security at every vertex is the present value of its future dividend stream over all succeeding vertices. The existence of such an equilibrium is proved under the following condition: continuous, weakly convex, strictly monotone and complete preferences, strictly positive endowments and dividends processes.
基金supported by the National Science Foundation (12001142)Harbin Normal University doctoral initiation Fund (XKB201812)supported by the Science Foundation Grant of Heilongjiang Province (LH2019A017)
文摘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)→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■ 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^(σ)=A+of A■.
