Stock loan valuation under a regime-switching model with mean-reverting and finite maturity

<正> Stock loans are business contracts between borrowers and lenders in which the borroweruses shares of stock as collateral for the loan.Since the value of the collateral is subject to wide andfrequent price swings,valuing such a transaction behaves more like an option pricing problem thana debt valuation problem.This paper will list,prove,and analyze formulas for stock loan valuationwith finite horizon under various stock models,including classical geometric Brownian motion,meanreverting,and two-state regime-switching with both mean-reverting and geometric Brownian motionstates.Numerical examples are reported to illustrate the results.     

Optimal control of multisolution ordinary differential equations in the absence of convexity

<正> In this paper,the authors study an optimal control problem governed by a class of multistateordinary differential equations in the absence of convexity.To overcome the difficulty that thecorresponding approximate optimal control problem may have no solution,relaxed controls are introduced.With the help of relaxation theory,Pontryagin's maximum principle for the optimal pairs ofthe original control problem is obtained.In the end of this paper,the authors discuss the applicationof the maximum principle by an example.     

Two-scale finite element Green’s function approximations with applications to electrostatic potential computation

<正> In this paper,a two-scale finite element approach is proposed and analyzed for approximationsof Green's function in three-dimensions.This approach is based on a two-scale finite elementspace defined,respectively,on the whole domain with size H and on some subdomain containing singularpoints with size h (h H).It is shown that this two-scale discretization approach is very efficient.In particular,the two-scale discretization approach is applied to solve Poisson-Boltzmann equationssuccessfully.     

A new approach of available transfer capability incorporating wind generation

The approach of available transfer capability (denoted as ATC) incorporating wind generation has been paid very high attention since the development of wind generation. Based on the maximum function, this paper presents an ATC model. The characteristic of the new model is twofold. First, it considers wind turbines connected to power system and static security of power system simultaneously. Second, it is a system of semismooth equations and can be solved easily. By using the smoothing strategy, a smoothing Newton method is adopted for solving the proposed new ATC model. Numerical simulation results of the IEEE 30-bus and 118-bus system show that the new model and algorithm are feasible and effective. The impact of wind turbines connected to power system on ATC is also analyzed.     

Optimal maintenance and replacement of extraction machinery

This paper considers a problem of optimal preventive maintenance and replacement schedule of equipment devoted to extracting resources from known deposits. Typical examples are oil drills, mine shovels, etc. At most one replacement of the existing machinery by a new one is allowed. The problem is formulated as an optimal control problem subject to the state constraint that the remaining deposit at any given time is nonnegative. We show that the optimal preventive maintenance, production rates, and the replacement and salvage times of the existing machinery and the new one, if required, can be obtained by solving sequentially a series of free-end-point optimal control problems. Moreover, an algorithm based on this result is developed and used to solve two illustrative examples.     

The distributed representation for societal risk classification toward BBS posts

The risk classification of BBS posts is important to the evaluation of societal risk level within a period. Using the posts collected from Tianya forum as the data source, the authors adopted the societal risk indicators from socio psychology, and conduct document-level multiple societal risk classification of BBS posts. To effectively capture the semantics and word order of documents, a shallow neural network as Paragraph Vector is applied to realize the distributed vector representations of the posts in the vector space. Based on the document vectors, the authors apply one classification method KNN to identify the societal risk category of the posts. The experimental results reveal that paragraph vector in document-level societal risk classification achieves much faster training speed and at least 10% improvements of F-measures than Bag-of-Words. Furthermore, the performance of paragraph vector is also superior to edit distance and Lucene-based search method. The present work is the first attempt of combining document embedding method with socio psychology research results to public opinions area.     

Null controllability of some degenerate wave equations

This paper is devoted to a study of the null controllability problems for one-dimensional linear degenerate wave equations through a boundary controller. First, the well-posedness of linear degenerate wave equations is discussed. Then the null controllability of some degenerate wave equations is established, when a control acts on the non-degenerate boundary. Different from the known controllability results in the case that a control acts on the degenerate boundary, any initial value in state space is controllable in this case. Also, an explicit expression for the controllability time is given. Furthermore, a counterexample on the controllability is given for some other degenerate wave equations.     

Continuity of solution mappings for parametric generalized set-valued weak vector equilibrium problems

This paper obtains some stability results for parametric generalized set-valued weak vector equilibrium problem. Under new assumptions, which do not contain any information about solution mappings, the authors establish the continuity of the solution mapping to a parametric generalized set-valued weak vector equilibrium problem without monotonicity. These results extend and improve some results in the literature. Some examples are given to illustrate the results.     

Positive observer design for positive Markovian jump systems with partly known transition rates

The paper is concerned with positive observer design for positive Markovian jump systems with partly known transition rates. By applying a linear co-positive type Lyapunov-Krasovskii function, a sufficient condition is proposed to ensure the stochastic stability of the error positive system and the existence of the positive observer, which is computed in linear programming. Finally, an example is given to demonstrate the validity of the main results.