This article studies optimal consumption-leisure, portfolio and retirement selection of an infinitely lived investor whose preference is formulated by a-maxmin expected CES utility which is to differentiate ambiguity ...This article studies optimal consumption-leisure, portfolio and retirement selection of an infinitely lived investor whose preference is formulated by a-maxmin expected CES utility which is to differentiate ambiguity and ambiguity attitude. Adopting the recursive multiple- priors utility and the technique of backward stochastic differential equations （BSDEs）, we transform the （^-maxmin expected CES utility into a classical expected CES utility under a new probability measure related to the degree of an investor＇s uncertainty. Our model investi- gates the optimal consumption-leisure-work selection, the optimal portfolio selection, and the optimal stopping problem. In this model, the investor is able to adjust her supply of labor flex- ibly above a certain minimum work-hour along with a retirement option. The problem can be analytically solved by using a variational inequality. And the optimal retirement time is given as the first time when her wealth exceeds a certain critical level. The optimal consumption-leisure and portfolio strategies before and after retirement are provided in closed forms. Finally, the distinctions of optimal consumption-leisure, portfolio and critical wealth level under ambiguity from those with no vagueness are discussed.展开更多
The goal of this paper is to investigate topological conditional pressure of a continuous transformation as defined for sub-additive potentials. This study presents a vari- ational inequality for sub-additive topologi...The goal of this paper is to investigate topological conditional pressure of a continuous transformation as defined for sub-additive potentials. This study presents a vari- ational inequality for sub-additive topological conditional pressure on a closed subset, which is the other form of the variational principle for the sub-additive topological pressure pre- sented by Cao, Feng, and Huang in [9]. Moreover, under some additional assumptions, this result can be generalized to the non-compact case.展开更多
This paper presents a modified domain decomposition method for the numerical solution of discrete Hamilton-Jacobi-Bellman equations arising from a class of optimal control problems using diffusion models. A convergenc...This paper presents a modified domain decomposition method for the numerical solution of discrete Hamilton-Jacobi-Bellman equations arising from a class of optimal control problems using diffusion models. A convergence theorem is established. Numerical results indicate the effectiveness and accuracy of the method.展开更多
A new hybrid projection iterative scheme is introduced to approximate a common element of the solution set of a generalized mixed equilibrium problem, the solution set of a variational inequality problem, and the set ...A new hybrid projection iterative scheme is introduced to approximate a common element of the solution set of a generalized mixed equilibrium problem, the solution set of a variational inequality problem, and the set of fixed points of a relatively weak nonexpansive mapping in the Banach spaces. The obtained results generalize and improve the recent results announced by many other authors.展开更多
This paper aims to study the solvability of vector Ky Fan inequalities and the compactness of its solution sets.For vector-valued functions with the cone semicontinuity and the cone quasiconvexity in infinite dimensio...This paper aims to study the solvability of vector Ky Fan inequalities and the compactness of its solution sets.For vector-valued functions with the cone semicontinuity and the cone quasiconvexity in infinite dimensional spaces,the authors prove some existence results of the solutions and the compactness of the solution sets.Especially,some results for the vector Ky Fan inequalities on noncompact sets are built and the compactness of its solution sets are also discussed.As applications,some existence theorems of the solutions of vector variational inequalities are obtained.展开更多
In this paper, anisotropic Crouzeix-Raviart type nonconforming finite element meth- ods are considered for solving the second order variational inequality with displacement obstacle. The convergence analysis is presen...In this paper, anisotropic Crouzeix-Raviart type nonconforming finite element meth- ods are considered for solving the second order variational inequality with displacement obstacle. The convergence analysis is presented and the optimal order error estimates are obtained under the hypothesis of the finite length of the free boundary. Numerical results are provided to illustrate the correctness of theoretical analysis.展开更多
Some block iterative methods for solving variational inequalities with nonlinear operators are proposed. Monotone convergence of the algorithms is obtained. Some comparison theorems are also established. Compared with...Some block iterative methods for solving variational inequalities with nonlinear operators are proposed. Monotone convergence of the algorithms is obtained. Some comparison theorems are also established. Compared with the research work in given by Pao in 1995 for nonlinear equations and research work in given by Zeng and Zhou in 2002 for elliptic variational inequalities, the algorithms proposed in this paper are independent of the boundedness of the derivatives of the nonlinear operator.展开更多
基金Supported by National Natural Science Foundation of China (71171003, 71271003)Programming Fund Project of the Humanities and Social Sciences Research of the Ministry of Education of China (12YJA790041)+1 种基金Anhui Natural Science Foundation (090416225, 1208085MG116)Anhui Natural Science Foundation of Universities (KJ2010A037, KJ2010B026)
文摘This article studies optimal consumption-leisure, portfolio and retirement selection of an infinitely lived investor whose preference is formulated by a-maxmin expected CES utility which is to differentiate ambiguity and ambiguity attitude. Adopting the recursive multiple- priors utility and the technique of backward stochastic differential equations （BSDEs）, we transform the （^-maxmin expected CES utility into a classical expected CES utility under a new probability measure related to the degree of an investor＇s uncertainty. Our model investi- gates the optimal consumption-leisure-work selection, the optimal portfolio selection, and the optimal stopping problem. In this model, the investor is able to adjust her supply of labor flex- ibly above a certain minimum work-hour along with a retirement option. The problem can be analytically solved by using a variational inequality. And the optimal retirement time is given as the first time when her wealth exceeds a certain critical level. The optimal consumption-leisure and portfolio strategies before and after retirement are provided in closed forms. Finally, the distinctions of optimal consumption-leisure, portfolio and critical wealth level under ambiguity from those with no vagueness are discussed.
基金supported by National University Student Innovation Program(111028508)supported by NSC Grant NSC 101-2115-M-034-001+1 种基金supported by NSFC(11371271)supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘The goal of this paper is to investigate topological conditional pressure of a continuous transformation as defined for sub-additive potentials. This study presents a vari- ational inequality for sub-additive topological conditional pressure on a closed subset, which is the other form of the variational principle for the sub-additive topological pressure pre- sented by Cao, Feng, and Huang in [9]. Moreover, under some additional assumptions, this result can be generalized to the non-compact case.
文摘This paper presents a modified domain decomposition method for the numerical solution of discrete Hamilton-Jacobi-Bellman equations arising from a class of optimal control problems using diffusion models. A convergence theorem is established. Numerical results indicate the effectiveness and accuracy of the method.
基金supported by the National Natural Science Foundation of China (No.11071169)supported by the Research Project of Shaoxing University(No.09LG1002)
文摘A new hybrid projection iterative scheme is introduced to approximate a common element of the solution set of a generalized mixed equilibrium problem, the solution set of a variational inequality problem, and the set of fixed points of a relatively weak nonexpansive mapping in the Banach spaces. The obtained results generalize and improve the recent results announced by many other authors.
基金supported by the Science and Technology Foundation of Guizhou Province under Grant No.20102133
文摘This paper aims to study the solvability of vector Ky Fan inequalities and the compactness of its solution sets.For vector-valued functions with the cone semicontinuity and the cone quasiconvexity in infinite dimensional spaces,the authors prove some existence results of the solutions and the compactness of the solution sets.Especially,some results for the vector Ky Fan inequalities on noncompact sets are built and the compactness of its solution sets are also discussed.As applications,some existence theorems of the solutions of vector variational inequalities are obtained.
文摘In this paper, anisotropic Crouzeix-Raviart type nonconforming finite element meth- ods are considered for solving the second order variational inequality with displacement obstacle. The convergence analysis is presented and the optimal order error estimates are obtained under the hypothesis of the finite length of the free boundary. Numerical results are provided to illustrate the correctness of theoretical analysis.
基金the National Natural Science Foundation of China(No.10671060)the Doctoral Fund of Ministry of Education of China granted[2003]0532006
文摘Some block iterative methods for solving variational inequalities with nonlinear operators are proposed. Monotone convergence of the algorithms is obtained. Some comparison theorems are also established. Compared with the research work in given by Pao in 1995 for nonlinear equations and research work in given by Zeng and Zhou in 2002 for elliptic variational inequalities, the algorithms proposed in this paper are independent of the boundedness of the derivatives of the nonlinear operator.
