Interest rate risk premium and equity valuation

<正> The authors employ the recent stochastic-control-based approach to financial mathematicsto solve a problem of determination of the risk premium for a stochastic interest rate model,andthe corresponding problem of equity valuation.The risk premium is determined explicitly,by meansof solving a corresponding partial differential equation (PDE),in two forms:one,time-dependent,corresponding to a finite time contract expiration,and the simpler version corresponding to perpetualcontracts.As stocks are perpetual contracts,when solving the problem of equity valuation,the latterform of the risk premium is used.By means of solving the general pricing PDE,an efficient equityvaluation method was developed that is a combination of some sophisticated explicit formulas,and anumerical procedure.     

Macroeconomic System Analysis On The Problem of Stagflation——The General Theory of Employment and Price (Ⅰ)

A system approach to building a theoretical model of macoecnomic system is shown in the paper. The IS-LM model, which is well-known in macroeconomics, is extended into a dynamic equilibrium model—IS-LM-AS model. The aggparative production function is a fresh deduced from a set of axioms. A comparative static analysis is carried out for evidence of the stagflation and the macroeconomic policy dilemma.     

Macroeconomic System Analysis on the Problem of Stagflation——The General Theory of Employment and Price (Ⅱ)

A system approach to building a theoretical model of macroeconomic system is shown in the paper. The IS-LM model, which is well-known in macroeconomics, is extended into a dynamic equilibrium model—IS-LM-AS model. The aggregate production function is afresh deduced from a set of axioms. A comparative static analysis is carried out for evidence of the stagflation and the macroeconomic policy dilemma.     

An Application of Fuzzy Decision Theory in Combat Decision Simulation

In this paper a model of military command process under the combat situation is presented. The model is based on the Lanchester Equations and Fuzzy Decision Theory. The decision of a military commander is usually a process from precise to fuzzy and then from fuzzy to precise,and the model fitted this process well. The model was used in a Warfare Simulation System whose object is to evaluate the effectiveness of the military C3I systems.     

Synchronization of chaos using radial basis functions neural networks

The Radial Basis Functions Neural Network （RBFNN） is used to establish the model of a response system through the input and output data of the system. The synchronization between a drive system and the response system can be implemented by employing the RBFNN model and state feedback control. In this case, the exact mathematical model, which is the precondition for the conventional method, is unnecessary for implementing synchronization. The effect of the model error is investigated and a corresponding theorem is developed. The effect of the parameter perturbations and the measurement noise is investigated through simulations. The simulation results under different conditions show the effectiveness of the method.     

Building a Tax Predictive Model Based on the Cloud Neural Network

Tax is very important to the whole country, so a scientific tax predictive model is needed. This paper introduces the theory of the cloud model. On this basis, it presents a cloud neural network, and analyzes the main factors which influence the tax revenue. Then if proposes a tax predictive model based on the cloud neural network. The model combines the strongpoints of the cloud model and the neural network. The experiment and simulation results show the ef-     

Collaborative optimization of maintenance and spare ordering of continuously degrading systems

A collaborative optimization model for maintenance and spare ordering of a single-unit degrading system is proposed in this paper based on the continuous detection. A gamma distribution is used to model the material degradation. The degrading decrement after the imperfect maintenance action is assumed as a random variable normal distribution. This model aims to obtain the optimal maintenance policy and spare ordering point with the expected cost rate within system lifecycle as the optimization objective. The rationality and feasibility of the model are proved through a numerical example.     

Cued search algorithm with uncertain detection performance for phased array radars

A cued search algorithm with uncertain detection performance is proposed for phased array radars. Firstly, a target search model based on the information gain criterion is presented with known detection performance, and the statistical characteristic of the detection probability is calculated by using the fluctuant model of the target radar cross section （RCS）. Secondly, when the detection probability is completely unknown, its probability density function is modeled with a beta distribution, and its posterior probability distribution with the radar observation is derived based on the Bayesian theory. Finally simulation results show that the cued search algorithm with a known RCS fluctuant model can achieve the best performance, and the algorithm with the detection probability modeled as a beta distribution is better than that with a random selected detection probability because the model parameters can be updated by the radar observation to approach to the real value of the detection probability.     

An analytic hierarchy process model of group consensus

In group decision making, a certain degree of consensus is necessary to derive a meaningful and valid outcome. This paper proposes a consensus reaching model for a group by using the Analytic Hierarchy Process （AHP）. It supports people to improve their group consensus level through an updating of their judgments. In this model, a moderator suggests the most discoraant aeclslon manet to update his judgment in each step. The proposed consensus reaching model allows decision makers to accept or reject the suggestion from the moderator. This model ensures that the judgment updating is effective and the final solution will be of acceptable consistency. Finally, a numerical example is given to illustrate the validity of the proposed consensus reaching model.     

A Model for Water Quality Assessment Based on the Information Entropy and Its Application in the Case of Huiji River

Based on the information entropy, a model for water quality assessment is Using this model, the paper gives a case study on the water quality assessment River. The space-time variation law of the water quality is analyzed also in this result indicates that the model possesses some clear mathematic and physical and it is simple, practical and accurate.     

Model algorithm control using neural networks for input delayed nonlinear control system

The performance of the model algorithm control method is partially based on the accuracy of the system’s model. It is difficult to obtain a good model of a nonlinear system, especially when the nonlinearity is high. Neural networks have the ability to "learn"the characteristics of a system through nonlinear mapping to represent nonlinear functions as well as their inverse functions. This paper presents a model algorithm control method using neural networks for nonlinear time delay systems. Two neural networks are used in the control scheme. One neural network is trained as the model of the nonlinear time delay system, and the other one produces the control inputs. The neural networks are combined with the model algorithm control method to control the nonlinear time delay systems. Three examples are used to illustrate the proposed control method. The simulation results show that the proposed control method has a good control performance for nonlinear time delay systems.     

面向飞推一体化的飞行器建模方法

The airbreathing hypersonic vehicle (ABHV) is a typical vehicle which has multidimensional nonlinear restrictions and intricate coupling. Due to the strong coupling interactions and multidimensional nonlinear restrictionists,the flight powered by scramjet is a critical phase of reference trajectory, guidance and control designing. Therefore, the development of a reasonable ABHV model is inevitable. The existing models of integrated aircraft scramjet are difficult for control design directly，and also can not be used with a numeric model together. To achieve the goal of exhuming the potential applications and expanding flight feasibility of ABHV,and improving the efficiency and robustness of ABHV from the overall level, based on the working mechanism and numerical model of scramjet, the performance and protected model of scramjet is researched, and the control oriented model of ABHV is developed.     

Novel magnetic field computation model in pattern classification

Field computation, an emerging computation technique, has inspired passion of intelligence science research. A novel field computation model based on the magnetic field theory is constructed. The proposed magnetic field computation （MFC） model consists of a field simulator, a non-derivative optimization algo- rithm and an auxiliary data processing unit. The mathematical model is deduced and proved that the MFC model is equivalent to a quadratic discriminant function. Furthermore, the finite element prototype is derived, and the simulator is developed, combining with particle swarm optimizer for the field configuration. Two benchmark classification experiments are studied in the numerical experiment, and one notable advantage is demonstrated that less training samples are required and a better generalization can be achieved.     

Modeling mechanism and extension of GM （1, 1）

Firstly,the research progress of grey model GM(1,1) is summarized,which is divided into three development stages: assimilation,alienation and melting stages.Then,the matrix analysis theory is used to study the modeling mechanism of GM(1,1),which decomposes the modeling data matrix into raw data transformation matrix,accumulated generating operation matrix and background value selection matrix.The changes of these three matrices are the essential reasons affecting the modeling and the accuracy of GM(1,1).Finally,the paper proposes a generalization grey model GGM(1,1),which is a extended form of GM(1,1) and also a unified form of model GM(1,1),model GM(1,1,α),stage grey model,hopping grey model,generalized accumulated model,strengthening operator model,weakening operator model and unequal interval model.And the theory and practical significance of the extended model is analyzed.     

Multi-dimensional scattering properties diagnosis system of scale aircraft model in an anechoic chamber

Aiming at the concept of ＂diagnosis＂, a simple and effective broadband radar cross section （RCS） measurement system is constructed, and some multi-dimensional scattering properties diagnosis techniques are presented based on the system. Firstly, a stepped-frequency signal is employed to achieve high range resolution, combining with a variety of signal processing tech- niques. Secondly, cross-range resolution is gained with a rotating table, and the high-resolution two-dimensional （2-D） imaging of the scale model is obtained by the microwave imaging theory. Finally, two receiving antennas with a small distance in altitude are used, and the three-dimensional （3-D） height distribution of scattering points on the scale model is extracted from the phase of images. Some typical bodies and a scale aircraft model are diagnosed in an anechoic chamber. The experimental results show that, after scaling with a metal sphere, the accurate one- dimensional （l-D） RCS pattern of the model is obtained, and it has a large dynamic range. When the bandwidth of the transmitting signal is 4 GHz, the resolution of the 2-D image can reach to 0.037 5 m. The 3-D height distribution of scattering points is given by interferometric measurement. This paper provides a feasible way to obtain high-precision scattering properties parameters of the scale aircraft model in a conventional rectangular anechoic chamber.     

Constrained predictive control based on T-S fuzzy model for nonlinear systems

A constrained generalized predictive control （GPC） algorithm based on the T-S fuzzy model is presented for the nonlinear system. First, a Takagi-Sugeno （T-S） fuzzy model based on the fuzzy cluster algorithm and the orthogonalleast square method is constructed to approach the nonlinear system. Since its consequence is linear, it can divide the nonlinear system into a number of linear or nearly linear subsystems. For this T-S fuzzy model, a GPC algorithm with input constraints is presented. This strategy takes into account all the constraints of the control signal and its increment, and does not require the calculation of the Diophantine equations. So it needs only a small computer memory and the computational speed is high. The simulation results show a good performance for the nonlinear systems.     

Learning algorithm and application of quantum BP neural networks based on universal quantum gates

A quantum BP neural networks model with learning algorithm is proposed. First, based on the universality of single qubit rotation gate and two-qubit controlled-NOT gate, a quantum neuron model is constructed, which is composed of input, phase rotation, aggregation, reversal rotation and output. In this model, the input is described by qubits, and the output is given by the probability of the state in which （1） is observed. The phase rotation and the reversal rotation are performed by the universal quantum gates. Secondly, the quantum BP neural networks model is constructed, in which the output layer and the hide layer are quantum neurons. With the application of the gradient descent algorithm, a learning algorithm of the model is proposed, and the continuity of the model is proved. It is shown that this model and algorithm are superior to the conventional BP networks in three aspects： convergence speed, convergence rate and robustness, by two application examples of pattern recognition and function approximation.     

ON AN SIS EPIDEMIC MODEL WITH STAGE STRUCTURE

A SIS infectious disease model with stage structure consisting of immature and mature stages is proposed using a discrete time delay. The aim of the paper is to investigate under which conditions the disease becomes endemic or not and to find the difference between the model with stage structure and the corresponding model without stage structure. It is shown that either there exists a unique endemic equilibrium point which is globally asymptotically stable or the disease dies out by using an iterative scheme. The effect of the time delay on the populations at equilibria is considered.     

Response surface method using grey relational analysis for decision making in weapon system selection

A proper weapon system is very important for a na- tional defense system. Generally, it means selecting the optimal weapon system among many alternatives, which is a multiple- attribute decision making （MADM） problem. This paper proposes a new mathematical model based on the response surface method （RSM） and the grey relational analysis （GRA）. RSM is used to obtain the experimental points and analyze the factors that have a significant impact on the selection results. GRA is used to an- alyze the trend relationship between alternatives and reference series. And then an RSM model is obtained, which can be used to calculate all alternatives and obtain ranking results. A real world application is introduced to illustrate the utilization of the model for the weapon selection problem. The results show that this model can be used to help decision-makers to make a quick comparison of alternatives and select a proper weapon system from multiple alternatives, which is an effective and adaptable method for solving the weapon system selection problem.     

Pricing Catastrophe Bond by Esscher Transform

This paper developed a model for pricing catastrophe bond whose trigger is loss index. In the model Esscher transform which is a facility usually used in actuarial science now provides an easy way to calculate Radon-Nikodym derivative so that the whole pricing process becomes easier to understand. At the end of this paper we use this model to price a China typhoon catastrophe bond which is also designed by us.