Application of Elzaki Transform Method to Market Volatility Using the Black-Scholes Model

Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of European Stock options and establish the theoretical foundation for Option pricing. Therefore, this paper evaluates the Black-Schole model in simulating the European call in a cash flow in the dependent drift and focuses on obtaining analytic and then approximate solution for the model. The work also examines Fokker Planck Equation (FPE) and extracts the link between FPE and B-SM for non equilibrium systems. The B-SM is then solved via the Elzaki transform method (ETM). The computational procedures were obtained using MAPLE 18 with the solution provided in the form of convergent series.

GENERAL BLACK-SCHOLES MODEL OF SECURITY VALUATION

This paper studies the multi-dimensional Black-Scholes model of security valnation. The extension of the Black-Scholes model implies; the partial differential equation derived from an absence of arbitrage which the authors solve by using the Feynmeu-Kac Formula. Then they compute its special example by solving the multi-variable partial differential equation.

Classification and Visualization of Surrounding Rock Mass Stability Based on Multi-Dimensional Cloud Model

The classification of the stability of surrounding rock is an uncertain system with multiple indices.The Multidimensional Cloud Model provides an advanced solution through the use of an improved model of One-dimensional Cloud Model.Setting each index as a one-dimensional attribute,the Multi-dimensional Cloud Model can set the digital characteristics of each index according to the cloud theory.The Multi-dimensional cloud generator can calculate the certainty of each grade,and then determine the stability levels of the surrounding rock according to the principle of maximum certainty.Using this model to 5 coal mine roadway surrounding rock examples and comparing the results with those of One-dimensional and Two-dimensional Cloud Models,we find that the Multi-dimensional Cloud Model can provide a more accurate solution.Since the classification results of the Multidimensional Cloud Model are difficult to be presented intuitively and visually,we reduce the Multi-dimensional Cloud Model to One-dimensional and Two-dimensional Cloud Models in order to visualize the results achieved by the Multi-dimensional Cloud Model.This approach provides a more accurate and intuitive method for the classification of the surrounding rock stability,and it can also be applied to other types of classification problems.

On discrete time hedging errors in a fractional Black-Scholes model

In this paper we investigate asymptotic behavior of error of a discrete time hedging strategy in a fractional Black-Scholes model in the sense of Wick-ItS-Skorohod integration. The rate of convergence of the hedging error due to discrete-time trading when the true strategy is known for the trader, is investigated. The result provides new statistical tools to study and detect the effect of the long-memory and the Hurst parameter for the error of discrete time hedging.

Option Pricing beyond Black-Scholes Model:Quantum Mechanics Approach

Based on the analog between the stochastic dynamics and quantum harmonic oscillator,we propose a market force driving model to generalize the Black-Scholes model in finance market.We give new schemes of option pricing,in which we can take various unexpected market behaviors into account to modify the option pricing.As examples,we present several market forces to analyze their effects on the option pricing.These results provide us two practical applications.One is to be used as a new scheme of option pricing when we can predict some hidden market forces or behaviors emerging.The other implies the existence of some risk premium when some unexpected forces emerge.

Multi-dimensional database design and implementation of dam safety monitoring system

To improve the effectiveness of dam safety monitoring database systems, the development process of a multi-dimensional conceptual data model was analyzed and a logic design wasachieved in multi-dimensional database mode. The optimal data model was confirmed by identifying data objects, defining relations and reviewing entities. The conversion of relations among entities to external keys and entities and physical attributes to tables and fields was interpreted completely. On this basis, a multi-dimensional database that reflects the management and analysis of a dam safety monitoring system on monitoring data information has been established, for which factual tables and dimensional tables have been designed. Finally, based on service design and user interface design, the dam safety monitoring system has been developed with Delphi as the development tool. This development project shows that the multi-dimensional database can simplify the development process and minimize hidden dangers in the database structure design. It is superior to other dam safety monitoring system development models and can provide a new research direction for system developers.

An Extension of the Black-Scholes and Margrabe Formulas to a Multiple Risk Economy

We consider an economic model with a deterministic money market account and a finite set of basic economic risks. The real-world prices of the risks are represented by continuous time stochastic processes satisfying a stochastic differential equation of diffusion type. For the simple class of log-normally distributed instantaneous rates of return, we construct an explicit state-price deflator. Since this includes the Black-Scholes and the Vasicek (Ornstein-Uhlenbeck) return models, the considered deflator is called Black-Scholes- Vasicek deflator. Besides a new elementary proof of the Black-Scholes and Margrabe option pricing formulas a validation of these in a multiple risk economy is achieved.

MULTI-DIMENSIONAL MARKOV CHAIN–BASED ANALYSIS OF CONFLICT PROBABILITY FOR SPECTRUM RESOURCE SHARING

In this paper, we consider the optimal problem of channels sharing with het-erogeneous traffic （real-time service and non-real-time service） to reduce the data conflict probability of users. Moreover, a multi-dimensional Markov chain model is developed to analyze the performance of the proposed scheme. Meanwhile, performance metrics are derived. Numerical results show that the proposed scheme can effectively reduce the forced termination probability, blocking probability and spectrum utilization.

A MULTISCALE MECHANICAL MODEL FOR MATERIALS BASED ON VIRTUAL INTERNAL BOND THEORY

Only two macroscopic parameters are needed to describe the mechanical properties of linear elastic solids, i.e. the Poisson＇s ratio and Young＇s modulus. Correspondingly, there should be two microscopic parameters to determine the mechanical properties of material if the macroscopic mechanical properties of linear elastic solids are derived from the microscopic level. Enlightened by this idea, a multiscale mechanical model for material, the virtual multi-dimensional internal bonds （VMIB） model, is proposed by incorporating a shear bond into the virtual internal bond （VIB） model. By this modification, the VMIB model associates the macro mechanical properties of material with the microscopic mechanical properties of discrete structure and the corresponding relationship between micro and macro parameters is derived. The tensor quality of the energy density function, which contains coordinate vector, is mathematically proved. From the point of view of VMIB, the macroscopic nonlinear behaviors of material could be attributed to the evolution of virtual bond distribution density induced by the imposed deformation. With this theoretical hypothesis, as an application example, a uniaxial compressive failure of brittle material is simulated. Good agreement between the experimental results and the simulated ones is found.

QoS Routing Algorithm with Multi-Dimensions for Overlay Networks

Overlay networks have emerged as a useful approach to providing a general framework for new applications and services that are to be implemented without significantly changing the IP-layer network infrastructure.Overlay routing has been used as an alternative to the default best effort Internet routing for the absence of end-to-end Quality of Service(QoS). While the former has recently been investigated, the conflict of QoS restraints and resource optimization remains unsolved. Recent studies have shown that overlay paths can give better latency, loss rate and TCP throughput. In this paper, a multi-dimensional QoS objective model based on the analysis of multiple QoS constraints has been presented, and a routing algorithm to optimise the overlay resource of its nodes and links is then proposed.In fact, the algorithm obtained multiple QoS values using probability theory to achieve the routing according to the multi-dimensional QoS objective vector of the QoS objective model. Simulation results reveals that the algorithm works better than other existing algorithms in balancing the network resources, and applications with stringent QoS requirements could be run.

Least squares fitting of coordinate parameters model

This paper starts with untime-diversification of the time-diversification deformation model and gives displacement distribution model of untime-diversification and simplifies further the study of deformation model. The paper discusses the problem of least squares fitting of coordinate parameters model—parameters of deformation model. During discussion, the basic means of cubic B splines and two steps of multidimensional disorder datum fitting are adopted which can make fitting function calculated mostly approximate coordinate parameters model and it can make calculation easier.

Research and implementation on multi-dimension trust evaluation method with web service

Integrating with practical e-commerce application, this paper introduces a novel multi-dimension evaluation method to depict and calculate the trust values. The multi-dimension evaluation metrics include functional and nonfunctional properties and corresponding weights. The continuous measurement values and the Markov chain mechanism are adopted to compute the trust value and detect the malicious behaviors. The current evaluation has larger influence factor on the next transaction behavior. A trust model is implemented with web service which consists of publication, filtrating, calculating and storage center. It is easily extended and the user only defines each property and its weights according to specific requirements, then the trust values are got. In order to conveniently manage and avoid the dead-lock, some constraint rules are proposed. The results show that the method based on multi-dimension can reflect objectively the dynamic change of trust values.

Application of PPE Model in Land Adaptability Appraisal in Small Basin Based on RAGA

The paper applies multi-dimension to lower technology-projection pursuit evaluation model in the conservation of water and soil discipline domain, optimizes the projection direction using the improved acceleration genetic algorithms, transforms the multi-dimensional data target to lower sub-space, and values soil adaptability of Dongdagou basin in Keshan County by searching the optimal projection direction and the projection function data. The paper provides a new notion and method for the conservation of water and soil in small basin.

Re-Establishing the Merits of Thermal Maturity and Petroleum Generation Multi-Dimensional Modeling with an Arrhenius Equation Using a Single Activation Energy

Thermal maturation and petroleum generation modeling of shales is essential for suc- cessful exploration and exploitation of conventional and unconventional oil and gas plays. For basin- wide unconventional resource plays such modeling, when well calibrated with direct maturity meas- urements from wells, can characterize and locate production sweet spots for oil, wet gas and dry gas. The transformation of kerogen to petroleum is associated with many chemical reactions, but models typically focus on first-order reactions with rates determined by the Arrhenius Equation. A miscon- ception has been perpetuated for many years that accurate thermal maturity modeling of vitrinite re- flectance using the Arrhenius Equation and a single activation energy, to derive a time-temperature index （~TTIARa）, as proposed by Wood （1988）, is flawed. This claim was initially made by Sweeney and Burnham （1990） in promoting their ＂EasyRo＂ method, and repeated by others. This paper dem- onstrates through detailed multi-dimensional burial and thermal modeling and direct comparison of the ~TTIARR and ＂EasyRo＂ methods that this is not the case. The ~TTIA^R method not only provides a very useful and sensitive maturity index, it can reproduce the calculated vitrinite reflectance values derived from models based on multiple activation energies （e.g., ＂EasyRo＂）. Through simple expres- sions the ~TTIAaa method can also provide oil and gas transformation factors that can be flexibly scaled and calibrated to match the oil, wet gas and dry gas generation windows. This is achieved in a more-computationally-efficient, flexible and transparent way by the ~TTIARR method than the ＂EasyRo＂ method. Analysis indicates that the ＂EasyRo＂ method, using twenty activation energies and a constant frequency factor, generates reaction rates and transformation factors that do not realisti- cally model observed kerogen behaviour and transformation factors over geologic time scales.

Non-selfsimilar Global Solutions and Their Structure for the Multi-dimensional Combustion Models

We investigate the Chapman-Jouguet model in multi-dimensional space, and construct explicitly its non-selfsimilar Riemann solutions. By the method we apply in this paper, general initial discontinuities can be dealt with, even for complex interaction of combustion waves. Furthermore, we analyze the way in which the area of unburnt gas shrinks.

A FAST AND HIGH ACCURACY NUMERICAL SIMULATION FOR A FRACTIONAL BLACK-SCHOLES MODEL ON TWO ASSETS

In this paper,a two dimensional(2D)fractional Black-Scholes(FBS)model on two assets following independent geometric Lévy processes is solved numerically.A high order convergent implicit difference scheme is constructed and detailed numerical analysis is established.The fractional derivative is a quasidifferential operator,whose nonlocal nature yields a dense lower Hessenberg block coefficient matrix.In order to speed up calculation and save storage space,a fast bi-conjugate gradient stabilized(FBi-CGSTAB)method is proposed to solve the resultant linear system.Finally,one example with a known exact solution is provided to assess the effectiveness and efficiency of the presented fast numerical technique.The pricing of a European Call-on-Min option is showed in the other example,in which the influence of fractional derivative order and volatility on the 2D FBS model is revealed by comparing with the classical 2D B-S model.

Enhancement of Proton Exchange Membrane Fuel Cell Performance Using a Novel Tapered Gas Channel

Based on use of multi-dimensional models,this investigation simulates the performance of a proton exchange membrane fuel cell by varying the channel pattern.In the one-dimensional model,the porosity of the gas diffusion layer is 0.3.The model reveals the water vapor distribution of the fuel cell and demonstrates that the amount of water vapor increases linearly with the reduction reaction adjacent to the gas channel and the gas diffusion layer.Secondly,four novel tapered gas channels are simulated by a two-dimensional model.The model considers the distributions of oxygen,the pressure drop,the amount of water vapor distribution and the polarization curves.The results indicate that as the channel depth decreases,the oxygen in the tapered gas channel can be accel-erated and forced into the gas diffusion layer to improve the cell performance.The three-dimensional model is employed to simulate the phenomenon associated with four novel tapered gas channels.The results also show that the best performance is realized in the least tapered gas channel.Finally,an experimentally determined mechanism is found to be consistent with the results of the simulation.

Multi-Dimensional Product Differentiation

We analyze product differentiation in a multi-dimensional model with non-uniform consumer distribution.The level of product differentiation is measured by both unit transport costs and firms'locations.Our analysis concerns both measures.First,fixing firms'locations,we show that equilibrium prices can increase or decrease with unit transport costs.The overall result depends on the interplay of a shifting effect and a rotating effect-the latter exists only in multi-dimensional models.Second,fixing unit transport costs,we find that under non-uniform distribution,there may exist no equilibrium where firms maximize differentiation on one dimension but minimize differentiation on other dimensions.Instead,there may exist an equilibrium where firms choose intermediate locations,contrary to common findings in existing studies which assume uniform distribution.

Optimized multi-dimensional optical storage reading strategy

A novel multi-dimensional （MD） optical storage was presented, which was realized by utilizing the space between tracks. Based on scalar diffraction theory, the channel bits parameters of the multi-dimensional optical storage were optimized, and the linear and nonlinear signals were analyzed accurately. Therefore, the format of the multi-dimensional optical disc was obtained, which makes the detection of readout signal easier. With respect to servo, coding and readout physics parameter of channel, the multi-dimensional optical disc is compatible with traditional disc such as Blu-ray disc （BD）. Also, the novel multi-dimensional optical storage is able to achieve a doubled density and a ten-fold readout data rate compared with traditional optical discs.

Recovery of Foreign Interest Rates from Exchange Binary Options

One of most challenging problems from applying the Black-Scholes model to financial derivatives, is reconciling the deviation between the expected and observed values. This study derives an extension of the Black-Scholes model and recovers the real drift of binary call options from their market prices. For space-dependent real drift, we obtain stable linearization and an integral equation. We also find that using market prices of options with different strike prices enables us to identify the term structure of the real drift. Results demonstrate that our new approach can confirm the existence of arbitrage opportunities in a binary option transaction.