This paper examines the existence of general equilibrium in a discrete time economy with the infinite horizon incomplete markets.There is a single good at each node in the event tree.The existence of general equilibri...This paper examines the existence of general equilibrium in a discrete time economy with the infinite horizon incomplete markets.There is a single good at each node in the event tree.The existence of general equilibrium for the infinite horizon economy is proved by taking limit of equilibria in truncated economies in which trade stops at a sequence of dates.展开更多
This paper studies the pricing and hedging for American contingent claims in an incom-plete market under mild conditions using the numeraire method to avoid changes of probabilitymeasure. When the market is incomplet...This paper studies the pricing and hedging for American contingent claims in an incom-plete market under mild conditions using the numeraire method to avoid changes of probabilitymeasure. When the market is incomplete, prices can not be derived by no-arbitrage arguments,since it is not possible to replicate the payoff of a given contingent claim by a controlled portfolioof the basic securitites. We adopt the method of fictitious completion of [1] to provide an upperbound and a lower bound for the actual market price of the claim.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
In this paper we investigate asymptotic behavior of error of a discrete time hedging strategy in a fractional Black-Scholes model in the sense of Wick-ItS-Skorohod integration. The rate of convergence of the hedging e...In this paper we investigate asymptotic behavior of error of a discrete time hedging strategy in a fractional Black-Scholes model in the sense of Wick-ItS-Skorohod integration. The rate of convergence of the hedging error due to discrete-time trading when the true strategy is known for the trader, is investigated. The result provides new statistical tools to study and detect the effect of the long-memory and the Hurst parameter for the error of discrete time hedging.展开更多
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
Motivated by financial and empirical arguments and in order to introduce a more flexible methodology of pricing,we provide a new approach to asset pricing based on Backward Volterra equations.The approach relies on an...Motivated by financial and empirical arguments and in order to introduce a more flexible methodology of pricing,we provide a new approach to asset pricing based on Backward Volterra equations.The approach relies on an arbitrage-free and incomplete market setting in continuous time by choosing non-unique pricing measures depending either on the time of evaluation or on the maturity of payoffs.We show that in the latter case the dynamics can be captured by a time-delayed backward stochastic Volterra integral equation here introduced which,to the best of our knowledge,has not yet been studied.We then prove an existence and uniqueness result for time-delayed backward stochastic Volterra integral equations.Finally,we present a Lucas-type consumption-based asset pricing model that justifies the emergence of stochastic discount factors matching the term structure of Sharpe ratios.展开更多
基金This research was supported by a project of Financial MathematicsFinancial Engineering and Finan-cial Managementwhich is o
文摘This paper examines the existence of general equilibrium in a discrete time economy with the infinite horizon incomplete markets.There is a single good at each node in the event tree.The existence of general equilibrium for the infinite horizon economy is proved by taking limit of equilibria in truncated economies in which trade stops at a sequence of dates.
文摘This paper studies the pricing and hedging for American contingent claims in an incom-plete market under mild conditions using the numeraire method to avoid changes of probabilitymeasure. When the market is incomplete, prices can not be derived by no-arbitrage arguments,since it is not possible to replicate the payoff of a given contingent claim by a controlled portfolioof the basic securitites. We adopt the method of fictitious completion of [1] to provide an upperbound and a lower bound for the actual market price of the claim.
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■.
基金Supported by the National Natural Science Foundation of China(11671115)the Natural Science Foundation of Zhejiang Province(LY14A010025)
文摘In this paper we investigate asymptotic behavior of error of a discrete time hedging strategy in a fractional Black-Scholes model in the sense of Wick-ItS-Skorohod integration. The rate of convergence of the hedging error due to discrete-time trading when the true strategy is known for the trader, is investigated. The result provides new statistical tools to study and detect the effect of the long-memory and the Hurst parameter for the error of discrete time hedging.
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Motivated by financial and empirical arguments and in order to introduce a more flexible methodology of pricing,we provide a new approach to asset pricing based on Backward Volterra equations.The approach relies on an arbitrage-free and incomplete market setting in continuous time by choosing non-unique pricing measures depending either on the time of evaluation or on the maturity of payoffs.We show that in the latter case the dynamics can be captured by a time-delayed backward stochastic Volterra integral equation here introduced which,to the best of our knowledge,has not yet been studied.We then prove an existence and uniqueness result for time-delayed backward stochastic Volterra integral equations.Finally,we present a Lucas-type consumption-based asset pricing model that justifies the emergence of stochastic discount factors matching the term structure of Sharpe ratios.