A class of nonlocal boundary value probl em s for elliptic systems in the unbounded domains are considered. Under suitable c onditions, the existence of solution and the comparison theorem for the boundary value prob...A class of nonlocal boundary value probl em s for elliptic systems in the unbounded domains are considered. Under suitable c onditions, the existence of solution and the comparison theorem for the boundary value problems are studied.展开更多
This paper investigates the maximal and minimal solutions of initial value problem for n-th order nonlinear integro-differential equations of Volterra type on an infinite interval in a Banach space by establishing a c...This paper investigates the maximal and minimal solutions of initial value problem for n-th order nonlinear integro-differential equations of Volterra type on an infinite interval in a Banach space by establishing a comparison result and using the monotone iterative technique.展开更多
We are concerned with the maximization of tr（V T AV）/tr（V T BV）＋tr（V T CV） over the Stiefel manifold {V ∈ R m×l ｜ V T V = Il} （l 〈 m）, where B is a given symmetric and positive definite matrix, A and...We are concerned with the maximization of tr（V T AV）/tr（V T BV）＋tr（V T CV） over the Stiefel manifold {V ∈ R m×l ｜ V T V = Il} （l 〈 m）, where B is a given symmetric and positive definite matrix, A and C are symmetric matrices, and tr（. ） is the trace of a square matrix. This is a subspace version of the maximization problem studied in Zhang （2013）, which arises from real-world applications in, for example, the downlink of a multi-user MIMO system and the sparse Fisher discriminant analysis in pattern recognition. We establish necessary conditions for both the local and global maximizers and connect the problem with a nonlinear extreme eigenvalue problem. The necessary condition for the global maximizers offers deep insights into the problem, on the one hand, and, on the other hand, naturally leads to a self-consistent-field （SCF） iteration to be presented and analyzed in detail in Part II of this paper.展开更多
This paper considers the problem about optimization of proportional reinsurance in the setting of diffusion models. The authors take into account non-cheap proportional reinsurance and bankruptcy value simultaneously....This paper considers the problem about optimization of proportional reinsurance in the setting of diffusion models. The authors take into account non-cheap proportional reinsurance and bankruptcy value simultaneously. The objective is to find the risk control policies which maximize the total discounted reserve and the bankruptcy value. Results show that, the optimal risk control policies and corresponding optimal return functions vary, depending both on the range of bankruptcy value and the relationship between the premium rate of insurance and that of reinsurance.展开更多
文摘A class of nonlocal boundary value probl em s for elliptic systems in the unbounded domains are considered. Under suitable c onditions, the existence of solution and the comparison theorem for the boundary value problems are studied.
文摘This paper investigates the maximal and minimal solutions of initial value problem for n-th order nonlinear integro-differential equations of Volterra type on an infinite interval in a Banach space by establishing a comparison result and using the monotone iterative technique.
基金supported by National Natural Science Foundation of China(Grant Nos.11101257 and 11371102)the Basic Academic Discipline Program+3 种基金the 11th Five Year Plan of 211 Project for Shanghai University of Finance and Economicsa visiting scholar at the Department of Mathematics,University of Texas at Arlington from February 2013 toJanuary 2014supported by National Science Foundation of USA(Grant Nos.1115834and 1317330)a Research Gift Grant from Intel Corporation
文摘We are concerned with the maximization of tr（V T AV）/tr（V T BV）＋tr（V T CV） over the Stiefel manifold {V ∈ R m×l ｜ V T V = Il} （l 〈 m）, where B is a given symmetric and positive definite matrix, A and C are symmetric matrices, and tr（. ） is the trace of a square matrix. This is a subspace version of the maximization problem studied in Zhang （2013）, which arises from real-world applications in, for example, the downlink of a multi-user MIMO system and the sparse Fisher discriminant analysis in pattern recognition. We establish necessary conditions for both the local and global maximizers and connect the problem with a nonlinear extreme eigenvalue problem. The necessary condition for the global maximizers offers deep insights into the problem, on the one hand, and, on the other hand, naturally leads to a self-consistent-field （SCF） iteration to be presented and analyzed in detail in Part II of this paper.
文摘This paper considers the problem about optimization of proportional reinsurance in the setting of diffusion models. The authors take into account non-cheap proportional reinsurance and bankruptcy value simultaneously. The objective is to find the risk control policies which maximize the total discounted reserve and the bankruptcy value. Results show that, the optimal risk control policies and corresponding optimal return functions vary, depending both on the range of bankruptcy value and the relationship between the premium rate of insurance and that of reinsurance.
