A new numerical method on American option pricing

Mathematically, the Black-Scholes model of American option pricing is a free boundary problem of partial differential equation. It is well known that this model is a nonlinear problem, and it has no closed form solution. We can only obtain an approximate solution by numerical method, but the precision and stability are hard to control, because the singularity at the exercise boundary near expiration date has a great effect on precision and stability for numerical method. We propose a new numerical method, FDA method, to solve the American option pricing problem, which combines advantages the Semi-Analytical Method and the Front-Fixed Difference Method. Using the FDA method overcomes the difficulty resulting from the singularity at the terminal of optimal exercise boundary. A large amount of calculation shows that the FDA method is more accurate and stable than other numerical methods.     

Stability analysis for an Euler-Bernoulli beam under local internal control and boundary observation

An Euler-Bernoulli beam system under the local internal distributed control and boundary point observation is studied. An infinite-dimensional observer for the open-loop system is designed. The closed-loop system that is non- dissipative is obtained by the estimated state feedback. By a detailed spectral analysis, it is shown that there is a set of generalized eigenfunctions, which forms a Riesz basis for the state space. Consequently, both the spectrum-determined growth condition and exponential stability are concluded.     

HAPE3D—a new constructive algorithm for the 3D irregular packing problem

We propose a new constructive algorithm, called HAPE3 D, which is a heuristic algorithm based on the principle of minimum total potential energy for the 3D irregular packing problem, involving packing a set of irregularly shaped polyhedrons into a box-shaped container with fixed width and length but unconstrained height. The objective is to allocate all the polyhedrons in the container, and thus minimize the waste or maximize profit. HAPE3 D can deal with arbitrarily shaped polyhedrons, which can be rotated around each coordinate axis at different angles. The most outstanding merit is that HAPE3 D does not need to calculate no-fit polyhedron(NFP), which is a huge obstacle for the 3D packing problem. HAPE3 D can also be hybridized with a meta-heuristic algorithm such as simulated annealing. Two groups of computational experiments demonstrate the good performance of HAPE3 D and prove that it can be hybridized quite well with a meta-heuristic algorithm to further improve the packing quality.     

High-gam adaptive regulator for a string equation with uncertain harmonic disturbance under boundary output feedback control

This paper considers the boundary stabilization and parameter estimation of a one-dimensional wave equation in the case when one end is fixed and control and hamaomc disturbance with uncertain amplitude are input at another end. A high-gain adaptive regulator is designed in terms of measured collocated end velocity. The existence and uniqueness of the classical solution ofthe closed-loop system is proven. It is shown that the state of the system approaches the standstill as time goes to infinity and mean-while, the estimated parameter converges to the unknown parameter.     

A Form-Correcting System of Chinese Characters Using a Model of Correcting Procedures of Calligraphists

A support system for form-correction of Chinese Characters is developed based upon a generation model SAM,and its feasibility is evaluated.SAM is excellent as a model for generating Chinese characters,but it is difficult to determine appropriate parameters because the use of calligraphic knowledge is needed.by noticing that calligraphic knowledge of calligraphists is included in their corrective actions, we adopt a strategy to acquire calligraphic knowledge by monitoring,recording and analyzing corrective actions of calligraphists,and try to realize an environment under which calligraphists can easily make corrections to character forms and which can record corrective actions of calligraphists without interfering with them.In this paper,we first construct a model of correcting procedures of calligraphists,which is composed of typical correcting procedures that are acquired by extensively observing their corrective actions and interviewing them,and develop a form-correcting system for brush-written Chinese characters by using the model.Secondly,through actual correcting experiments,we demonstrate that parameters within SAM can be easily corrected at the level of character patterns by our system,and show that it is effective and easy for calligraphists to be used by evaluating effectiveness of the correcting model,sufficiency of its functions and execution speed.     

Exponential nonlinear observer based on the differential state-dependent Riccati equation

This paper presents a novel nonlinear continuous-time observer based on the differential state-dependent Riccati equation(SDRE) filter with guaranteed exponential stability.Although impressive results have rapidly emerged from the use of SDRE designs for observers and filters,the underlying theory is yet scant and there remain many unanswered questions such as stability and convergence.In this paper,Lyapunov stability analysis is utilized in order to obtain the required conditions for exponential stability of the estimation error dynamics.We prove that under specific conditions,the proposed observer is at least locally exponentially stable.Moreover,a new definition of a detectable state-dependent factorization is introduced,and a close relation between the uniform detectability of the nonlinear system and the boundedness property of the state-dependent differential Riccati equation is established.Furthermore,through a simulation study of a second order nonlinear model,which satisfies the stability conditions,the promising performance of the proposed observer is demonstrated.Finally,in order to examine the effectiveness of the proposed method,it is applied to the highly nonlinear flux and angular velocity estimation problem for induction machines.The simulation results verify how effectively this modification can increase the region of attraction and the observer error decay rate.     

An Analysis of Newly Built Forecasting Method to the Sanitary Materials Data

Correct sales forecasting is inevitable in industries. In industries, how to improve forecasting accuracy such as sales, shipping is an important issue. There are many researches made on this. In this paper, a hybrid method is introduced and plural methods are compared. Focusing that the equation of ESM （exponential smoothing method） is equivalent to （1,1） order ARMA model equation, a new method of estimation of smoothing constant in exponential smoothing method is proposed before by us which satisfies minimum variance of forecasting error. In this paper, trend removing by the combination of linear and 2nd order non-linear function and 3rd order non-linear function is carried out to the manufacturer＇s data of sanitary materials. The new method shows that it is useful for the time series that has various trend characteristics and rather strong seasonal trend. The effectiveness of this method should be examined in various cases.     

Preparing Mathematical Equations in a Document Preparation Environment

WITS－Math is a mathematical equation formatting tool in WITS,a multilingual document preparation environment.WITS-Math includes a library manager and an equation formatter.The main task of WITS-Math is to format diversities of mathematical equations and organize them into an equation library used by other tools in the WITS environment.WITS-Math is a direct manipulation mathematics editor.It uses syntax directed markup language as the internal representation,and provides an interactive WYSI-WYG interface for users to format equations.WITS-Math provides an equation access mechanism.Other tools can access equations in a library br cross-reference from a source file or through data exchange without knowing the structure of equation libraries.The common data structure and the rendering object in the WITS platform ensure that the formatted equations can be directly used by other tools.     

New synthesis algorithm of static output feedback sliding mode control for a class of uncertain systems

Based on a kind of regular form,a Lyapunov matrix with special structure is presented to design the sliding surface matrix conveniently and then an effective algorithm is developed on it. A simple static output feedback sliding mode control law without extra dynamic equation is given, such that the predefined shding surface is reached in finite time for the general matching uncertainties. In the reported result, this extra dynamic equation is used for evaluating the norm bound of the unmeasured state vector. Finally, some examples are studied to illustrate the proposed approach.     

Relationship Between Support Vector Set and Kernel Functions in SVM

Based on a constructive learning approach,covering algorithms,we investigate the relationship between support vector sets and kernel functions in support vector machines (SVM).An interesting result is obtained.That is,in the linearly non-separable case,any sample of a given sample set K can become a support vector under a certain kernel function.The result shows that when the sample set K is linearly non-separable,although the chosen kernel function satisfies Mercer‘s condition its corresponding support vector set is not necessarily the subset of K that plays a crucial role in classifying K.For a given sample set,what is the subset that plays the crucial role in classification?In order to explore the problem,a new concept,boundary or boundary points,is defined and its properties are discussed.Given a sample set K,we show that the decision functions for classifying the boundary points of K are the same as that for classifying the K itself.And the boundary points of K only depend on K and the structure of the space at which k is located and independent of the chosen approach for finding the boundary.Therefore,the boundary point set may become the subset of K that plays a crucial role in classification.These results are of importance to understand the principle of the support vector machine(SVM) and to develop new learning algorithms.     

Consistency Property of Finite FC-Normal Logic Programs

Marek＇s forward-chaining construction is one of the important techniques for investigating the non-monotonic reasoning. By introduction of consistency property over a logic program, they proposed a class of logic programs, FC-normal programs, each of which has at least one stable model. However, it is not clear how to choose one appropriate consistency property for deciding whether or not a logic program is FC-normal. In this paper, we firstly discover that, for any finite logic programⅡ, there exists the least consistency property LCon（Ⅱ） overⅡ, which just depends onⅡitself, such that, Ⅱ is FC-normal if and only ifⅡ is FC-normal with respect to （w.r.t.） LCon（Ⅱ）. Actually, in order to determine the FC-normality of a logic program, it is sufficient to check the monotonic closed sets in LCon（Ⅱ） for all non-monotonic rules, that is LFC（Ⅱ）. Secondly, we present an algorithm for computing LFC（Ⅱ）. Finally, we reveal that the brave reasoning task and cautious reasoning task for FC-normal logic programs are of the same difficulty as that of normal logic programs.     

Optimal Synchronization Control of Heterogeneous Asymmetric Input-Constrained Unknown Nonlinear MASs via Reinforcement Learning

The asymmetric input-constrained optimal synchronization problem of heterogeneous unknown nonlinear multiagent systems(MASs)is considered in the paper.Intuitively,a state-space transformation is performed such that satisfaction of symmetric input constraints for the transformed system guarantees satisfaction of asymmetric input constraints for the original system.Then,considering that the leader’s information is not available to every follower,a novel distributed observer is designed to estimate the leader’s state using only exchange of information among neighboring followers.After that,a network of augmented systems is constructed by combining observers and followers dynamics.A nonquadratic cost function is then leveraged for each augmented system(agent)for which its optimization satisfies input constraints and its corresponding constrained Hamilton-Jacobi-Bellman(HJB)equation is solved in a data-based fashion.More specifically,a data-based off-policy reinforcement learning(RL)algorithm is presented to learn the solution to the constrained HJB equation without requiring the complete knowledge of the agents’dynamics.Convergence of the improved RL algorithm to the solution to the constrained HJB equation is also demonstrated.Finally,the correctness and validity of the theoretical results are demonstrated by a simulation example.     

A neuro-fuzzy-sliding mode controller using nonlinear sliding surface applied to the coupled tanks system

The aim of this paper is to develop a neuro-fuzzy-sliding mode controller （NFSMC） with a nonlinear sliding surface for a coupled tank system. The main purpose is to eliminate the chattering phenomenon and to overcome the problem of the equivalent control computation. A first-order nonlinear sliding surface is presented, on which the developed sliding mode controller （SMC） is based. Mathematical proof for the stability and convergence of the system is presented. In order to reduce the chattering in SMC, a fixed boundary layer around the switch surface is used. Within the boundary layer, where the fuzzy logic control is applied, the chattering phenomenon, which is inherent in a sliding mode control, is avoided by smoothing the switch signal. Outside the boundary, the sliding mode control is applied to drive the system states into the boundary layer. Moreover, to compute the equivalent controller, a feed-forward neural network （NN） is used. The weights of the net are updated such that the corrective control term of the NFSMC goes to zero. Then, this NN also alleviates the chattering phenomenon because a big gain in the corrective control term produces a more serious chattering than a small gain. Experimental studies carried out on a coupled tank system indicate that the proposed approach is good for control applications.     

Chaotic vibration of the one-dimensional linear wave equation with a van der Pol nonlinear boundary condition

The one-dimensional linear wave equation with a van der Pol nonlinear boundary condition is one of the simplest models that may cause isotropic or nonisotropic chaotic vibrations. It characterizes the nonisotropic chaotic vibration by means of the total variation theory. Some results are derived on the exponential growth of total variation of the snapshots on the spatial interval in the long-time horizon when the map and the initial condition satisfy some conditions.     

A Hybrid Method to Improve Forecasting AccuracymAn Application to the Canned Cooked Rice and the Aseptic Packaged Rice

In industries, how to improve forecasting accuracy, such as sales, shipping, is an important issue. In this paper, a hybrid method is introduced and plural methods are compared. Focusing that the equation of ESM （exponential smoothing method） is equivalent to （1, 1） order ARMA Model （autoregressive moving average model） equation, new method of estimation of smoothing constant in exponential smoothing method is proposed before by us which satisfies minimum variance of forecasting error. Trend removing by the combination of linear and 2nd order non-linear function and 3rd order non-linear function is executed to the original production data of two kinds of cooked rice （canned rice and aseptic packaged rice）. Genetic algorithm is utilized to search the optimal weight for the weighting parameters of linear and non-linear function. For the comparison, monthly trend is removed after that. The new method shows that it is useful for the time series that has various trend characteristics and has rather strong seasonal trend.     

A new approach on designing l1 optimal regulator with minimum order for SISO linear systems

For a SISO linear discrete-time system with a specified input signal, a novel method to realize optimal l1 regulation control is presented. Utilizing the technique of converting a polynomial equation to its corresponding matrix equation, a linear programming problem to get an optimal l1 norm of the system output error map is developed which includes the first term and the last term of the map sequence in the objective function and the right vector of its constraint matrix equation, respectively. The adjustability for the width of the constraint matrix makes the trade-off between the order of the optimal regulator and the value of the minimum objective norm become possible, especially for achieving the optimal regulator with minimum order. By norm scaling rules for the constraint matrix equation, the optimal solution can be scaled directly or be obtained by solving a linear programming problem with l\ norm objective.     

Improvements to the Control Techniques of Sequential Inference Machines——from Instructions to Hardware Organization

Nondeterminism of PROLOG execution requires that a block of control information or a choicepoint for each procedure call be stored when there are other candidate clauses to be used.Whenthe currently selected clause fails,the bindings made by the clause must be undone and the storedchoice point is reactivated,and then another clause of the candidate ones is chosen to run on it.Storing and reactivating choice points and undoing account for the great overhead are required tocontrol PROLOG execution,which is quite different from conventional programs.This paper focuses on the techniques used in Sequential PROLOG Engine(SPE)to reduce theoverhead of control operations.The control instructions of SPE store no more choice points thanthe necessary.Its architecture takes the approaches of analysing the potential parallelism in the con-trol operations and developing a fraction of it due to the cost-effect consideration.The results ofexecuting two sample programs on SPE in the form of hand timings are presented,which favor theapproach.     

A robust test of uncertain linear systems

In this paper, it is shown that for low-order uncertain systems, there is no need to calculate all the minimum and maximum values of the coefficients for a perturbed system which is expressed in terms of polynomials and hence no need to formulate and test all the four Kharitonov＇s polynomials. Furthermore, for higher-order systems such as n ≥ 5, the usual four Kharitonov＇s polynomials need not be tested initially for sufficient condition of perturbed systems; rather, the necessary condition can be checked before going for sufficient condition. In order to show the effectiveness of the proposed method, numerical examples are shown and computational efficiency is highlighted.