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.

Evaluation of Nonbreaking Wave-Induced Mixing Parameterization Schemes Based on a One-Dimensional Ocean Model

Surface waves have a considerable effect on vertical mixing in the upper ocean.In the past two decades,the vertical mixing induced through nonbreaking surface waves has been used in ocean and climate models to improve the simulation of the upper ocean.Thus far,several nonbreaking wave-induced mixing parameterization schemes have been proposed;however,no quantitative comparison has been performed among them.In this paper,a one-dimensional ocean model was used to compare the performances of five schemes,including those of Qiao et al.(Q),Hu and Wang(HW),Huang and Qiao(HQ),Pleskachevsky et al.(P),and Ghantous and Babanin(GB).Similar to previous studies,all of these schemes can decrease the simulated sea surface temperature(SST),increase the subsurface temperature,and deepen the mixed layer,thereby alleviating the common thermal deviation problem of the ocean model for upper ocean simulation.Among these schemes,the HQ scheme exhibited the weakest wave-induced mixing effect,and the HW scheme exhibited the strongest effect;the other three schemes exhibited roughly the same effect.In particular,the Q and P schemes exhibited nearly the same effect.In the simulation based on observations from the Ocean Weather Station Papa,the HQ scheme exhibited the best performance,followed by the Q scheme.In the experiment with the HQ scheme,the root-mean-square deviation of the simulated SST from the observations was 0.43℃,and the mixed layer depth(MLD)was 2.0 m.As a contrast,the deviations of the SST and MLD reached 1.25℃ and 8.4 m,respectively,in the experiment without wave-induced mixing.

IAP General Circulation Models: A First Step Towards Developing a Local Area Model for Weather Prediction in Nigeria

In an earlier study, the Atmospheric Models Intercomparison Program (AMIP) simulations of African climate using the nine-layer gridpoint atmospheric general circulation model were found to be closely related to the observed European Centre for Medium Range Weather Forecast (ECMWF) temperature data at 500 and 850 hPa. This paper presents the analysis of the simulation of African climate using the Global Ocean-Atmosphere-Land System Model (IAP/LASG GOALS) and the nine-layer spectral general circulation model rhomboidally truncated at zonal wave number 15 (L9R15) developed at the Institute of Atmospheric Physics (IAP), Chinese Academy of Sciences, Beijing. Both model simulations were not significantly different from the National Center for Environmental Prediction (NCEP) Reanalysis monthly mean data for 1980-1995 in the case of surface air temperature, sea level pressure and precipitation, with the GOALS reproducing the seasonal mean climate over Africa better. The implications of the encouraging results in developing a local area model for Nigeria have been discussed. The great role of topography in the developing of general circulation models for numerical modelling of weather and climate has been stressed.

Deterministic and Stochastic Schistosomiasis Models with General Incidence

In this paper, deterministic and stochastic models for schistosomiasis involving four sub-populations are developed. Conditions are given under which system exhibits thresholds behavior. The disease-free equilibrium is globally asymptotically stable if R0 ?and the unique endemic equilibrium is globally asymptotically stable when R0 >?1. The populations are computationally simulated under various conditions. Comparisons are made between the deterministic and the stochastic model.

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.

Analysis of the History and Current Situation of the Development of General Practice Teaching Clinics in China

A summary of the exploration of the teaching mode of the general practice teaching clinic, a summary of the deficiencies of the teaching clinic and a summary of the significance of the establishment of the general practice teaching clinic are presented with a view to promoting the development of general practice and cultivating more excellent successors in general practice.

Distribution of Mass and Energy in Five General Cosmic Models

Distributions of the universe horizon distance and universe horizon volume were investigated in the light of five general cosmic models which were constructed in a previous study. Both distributions increase so slowly up to t ≈ 21.5444 Myr, then they start raising very fast up to t ≈ 60 Gyr. Afterwards, they increase again very slowly until t ≈ 124 Gyr. Distributions of mass of radiation, matter and dark energy within the horizon volume of the universe were also studied in the five general cosmic models. The masses of both radiation and matter decrease gradually with time while the mass of dark energy increases. The mass of radiation prevailed in the early universe up to t ≈ 34627.5 - 55916.2 yr, where it becomes equal to the mass of matter. Then the mass of matter dominated until t ≈ 9.4525 - 10.0632 Gyr, where it becomes equal to the mass of dark energy. Thenceforward, the mass of dark energy prevails the universe. The cosmic space becomes approximately matter empty in the so far future of the universe.

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.

Calculation of the Standard Model Parameters and Particles Based on a SU(4) Preon Model

This paper describes an extension and a new foundation of the Standard Model of particle physics based on a SU(4)-force called hyper-color, and on preon subparticles. The hyper-color force is a generalization of the SU(2)-based weak interaction and the SU(1)-based right-chiral self-interaction, in which the W-and the Z-bosons are Yukawa residual-field-carriers of the hyper-color force, in the same sense as the pions are the residual-field-carriers of the color SU(3) interaction. Using the method of numerical minimization of the SU(4)-action based on this model, the masses and the inner structure of leptons, quarks and weak bosons are calculated: the mass results are very close to the experimental values. We calculate also precisely the value of the Cabibbo angle, so the mixing matrices of the Standard model, CKM matrix for quarks and PMNS matrix for neutrinos can also be calculated. In total, we reduce the 29 parameters of the Standard Model to a total of 7 parameters.

Fundamental Framework and Experiments of the ThirdGeneration of IAP/LASG World OceanGeneral Circulation Model

A new generation of the IAP / LASG world ocean general circulation model is designed and presented based on the previous 20-layer model, with enhanced spatial resolutions and improved parameterizations. The model uses a triangular-truncated spectral horizontal grid system with its zonal wave number of 63 (T63) to match its atmospheric counterpart of a T63 spectral atmosphere general circulation model in a planned coupled ocean-atmosphere system. There are 30 layers in vertical direction, of which 20 layers are located above 1000 m for better depicting the permanent thermocline. As previous ocean models developed in IAP / LASG, a free surface (rather than “rigid-lid” approximation) is included in this model. Compared with the 20-layer model, some more detailed physical parameterizations are considered, including the along / cross isopycnal mixing scheme adapted from the Gent-MacWilliams scheme. The model is spun up from a motionless state. Initial conditions for temperature and salinity are taken from the three-dimensional distributions of Levitus’ annual mean observation. A preliminary analysis of the first 1000-year integration of a control experiment shows some encouraging improvements compared with the twenty-layer model, particularly in the simulations of permanent thermocline, thermohaline circulation, meridional heat transport, etc. resulted mainly from using the isopycnal mixing scheme. However, the use of isopycnal mixing scheme does not significantly improve the simulated equatorial thermocline. A series of numerical experiments show that the most important contribution to the improvement of equatorial thermocline and the associated equatorial under current comes from reducing horizontal viscosity in the equatorial regions. It is found that reducing the horizontal viscosity in the equatorial Atlantic Ocean may slightly weaken the overturning rate of North Atlantic Deep Water.

An Eddy-Permitting Oceanic General Circulation Model and Its Preliminary Evaluation

An eddy-permitting, quasi-global oceanic general circulation model, LICOM (LASG/IAP (State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics) Climate System Ocean Model), with a uniform grid of 0.5? × 0.5? is established. Forced by wind stresses from Hellerman and Rosenstain (1983), a 40-yr integration is conducted with sea surface temperature and salinity being restored to the Levitus 94 datasets. The evaluation of the annual mean climatology of the LICOM control run shows that the large-scale circulation can be well reproduced. A comparison between the LICOM control run and a parallel integration of L30T63, which has the same framework but a coarse resolution, is also made to con?rm the impact of resolution on the model performance. On account of the reduction of horizontal viscosity with the enhancement of the horizontal resolution, LICOM improves the simulation with respect to not only the intensity of the large scale circulations, but also the magnitude and structure of the Equatorial Undercurrent and South Equatorial Current. Taking advantage of the ?ne grid size, the pathway of the Indonesian Through?ow (ITF) is better represented in LICOM than in L30T63. The transport of ITF in LICOM is more convergent in the upper layer. As a consequence, the Indian Ocean tends to get warmer in LICOM. The poleward heat transports for both the global and individual basins are also signi?cantly improved in LICOM. A decomposed analysis indicates that the transport due to the barotropic gyre, which primarily stands for the barotropic e?ect of the western boundary currents, plays a crucial role in making the di?erence.

A Nine-layer Atmospheric General Circulation Model and Its Performance

Different versions of a new nine-layer general circulation model which is rhomboidally truncated at zonal wavenumber 15(L9R15)are introduced in this paper.On using the observed global monthly sea surfaCe temperature(SST)and sea ice(SI)data from 1979 to 1988 offered by the internahonal Atmospheric Model Iute-comparison Program(AMIP),these different model versions were integrated for the ten-year AMIP period. Results show that the model iscapable of simulating the basic states of the atmosphere and its interannual variability,and in performing reasonablesensitivity experiments.

Dynamical Framework of IAP Nine-Level Atmospheric General Circulation Model

The dynamical framework of the nine-level version of the IAP AGCM is presented in this paper. The emphasis of the model's description is put on the following two aspects:(1) A model's standard atmosphere, which is a satisfactory approximation to the observed troposphere and lower stratosphere standard atmosphere, is introduced into the equations of the model to permit a more accurate calculation of the vertical transport terms, especially near the tropopause; (2) The vertical levels of the model are carefully selected to guarantee a smooth dependence of layer thickness upon pressure in order to reduce the truncation error involved in the unequal interval vertical finite-differencing. For testing the model, two kinds of linear baroclinic Rossby-Haurwitz waves, one of which has a dynamically stable vertical structure and the other has a relatively unstable one, are constructed to provide initial conditions for numerical experiments. The two waves have been integrated for more than 300 days and 100 days respectively by using the model and both of them are propagating westward with almost identical phase-speed during the time period of the integrations. No obvious change of the wave patterns is found at the levels in the model's troposphere. The amplitudes of both two waves at the uppermost level, however, exhibit rather significant oscillation with time, of which the periods are exactly 20 days and 25 days espectively.The explanation of this interesting phenomena is still under investigation.

A Numerical World Ocean General Circulation Model

This paper describes a numerical model of the world ocean based on the fully primitive equations. A 'Standard' ocean state is introduced into the equations of the model and the perturbed thermodynamic variables are used in the modlc's calculations. Both a free upper surface and a bottom topography are included in the model and a sigma coordinate is used to normalize the model's vertical component. The model has four unevenly-spaced layers and 4 × 5 horizontal resolution based on C-grid system. The finite-difference scheme of the model is designed to conserve the gross available energy in order to avoid fictitious energy generation or decay.The model has been tested in response to the annual mean surface wind stress, sea level air pressure and sea level air temperature as a preliminary step to its further improvement and its coupling with a global atmospheric general circulation model. Some of results, including currents, temperature and sea surface elevation simulated by the mode! arc presented.

A Study on Sulfate Optical Properties and Direct Radiative Forcing Using LASG-IAP General Circulation Model

The direct radiative forcing （DRF） of sulfate aerosols depends highly on the atmospheric sulfate loading and the meteorology, both of which undergo strong regional and seasonal variations. Because the optical properties of sulfate aerosols are also sensitive to atmospheric relative humidity, in this study we first examine the scheme for optical properties that considers hydroscopic growth. Next, we investigate the seasonal and regional distributions of sulfate DRF using the sulfate loading simulated from NCAR CAM-Chem together with the meteorology modeled from a spectral atmospheric general circulation model （AGCM） developed by LASG-IAP. The global annual-mean sulfate loading of 3.44 mg m-2 is calculated to yield the DRF of -1.03 and -0.57 W m-2 for clear-sky and all-sky conditions, respectively. However, much larger values occur on regional bases. For example, the maximum all-sky sulfate DRF over Europe, East Asia, and North America can be up to -4.0 W m-2. The strongest all-sky sulfate DRF occurs in the Northern Hemispheric July, with a hemispheric average of -1.26 W m-2. The study results also indicate that the regional DRF are strongly affected by cloud and relative humidity, which vary considerably among the regions during different seasons. This certainly raises the issue that the biases in model-sinmlated regional meteorology can introduce biases into the sulfate DRF. Hence, the model processes associated with atmospheric humidity and cloud physics should be modified in great depth to improve the simulations of the LASG-IAP AGCM and to reduce the uncertainty of sulfate direct effects on global and regional climate in these simulations.

Energy Model for UAV Communications:Experimental Validation and Model Generalization

Wireless communication involving unmanned aerial vehicles(UAVs)is expected to play an important role in future wireless networks.However,different from conventional terrestrial communication systems,UAVs typically have rather limited onboard energy on one hand,and require additional flying energy consumption on the other hand.This renders energy-efficient UAV communication with smart energy expenditure of paramount importance.In this paper,via extensive flight experiments,we aim to firstly validate the recently derived theoretical energy model for rotary-wing UAVs,and then develop a general model for those complicated flight scenarios where rigorous theoretical model derivation is quite challenging,if not impossible.Specifically,we first investigate how UAV power consumption varies with its flying speed for the simplest straight-and-level flight.With about 12,000 valid power-speed data points collected,we first apply the model-based curve fitting to obtain the modelling parameters based on the theoretical closed-form energy model in the existing literature.In addition,in order to exclude the potential bias caused by the theoretical energy model,the obtained measurement data is also trained using a model-free deep neural network.It is found that the obtained curve from both methods can match quite well with the theoretical energy model.Next,we further extend the study to arbitrary 2-dimensional(2-D)flight,where,to our best knowledge,no rigorous theoretical derivation is available for the closed-form energy model as a function of its flying speed,direction,and acceleration.To fill the gap,we first propose a heuristic energy model for these more complicated cases,and then provide experimental validation based on the measurement results for circular level flight.

Primary Reasoning behind the Double ITCZ Phenomenon in a Coupled Ocean-Atmosphere General Circulation Model

This paper investigates the processes behind the double ITCZ phenomenon, a common problem in Coupled ocean-atmosphere General Circulation Models (CGCMs), using a CGCM—FGCM-0 (Flexible General Circulation Model, version 0). The double ITCZ mode develops rapidly during the ?rst two years of the integration and becomes a perennial phenomenon afterwards in the model. By way of Singular Value Decomposition (SVD) for SST, sea surface pressure, and sea surface wind, some air-sea interactions are analyzed. These interactions prompt the anomalous signals that appear at the beginning of the coupling to develop rapidly. There are two possible reasons, proved by sensitivity experiments: (1) the overestimated east-west gradient of SST in the equatorial Paci?c in the ocean spin-up process, and (2) the underestimated amount of low-level stratus over the Peruvian coast in CCM3 (the Community Climate Model, Version Three). The overestimated east-west gradient of SST brings the anomalous equatorial easterly. The anomalous easterly, a?ected by the Coriolis force in the Southern Hemisphere, turns into an anomalous westerly in a broad area south of the equator and is enhanced by atmospheric anomalous circulation due to the underestimated amount of low-level stratus over the Peruvian coast simulated by CCM3. The anomalous westerly leads to anomalous warm advection that makes the SST warm in the southeast Paci?c. The double ITCZ phenomenon in the CGCM is a result of a series of nonlocal and nonlinear adjustment processes in the coupled system, which can be traced to the uncoupled models, oceanic component, and atmospheric component. The zonal gradient of the equatorial SST is too large in the ocean component and the amount of low-level stratus over the Peruvian coast is too low in the atmosphere component.

A Coupled General Circulation Model for the Tropical Pacific Ocean and Global Atmosphere

On the basis of Zeng's theorehcal design, a coupled general circulation model(CGCM) is develO￣ with itscharacteristics different from other CGCMs such as the unified vertical coordinates and subtraction of the standard stratification for both atmosphere and ocean, available energy consideration,and so on.The oceanic comPOnent is a free surface tropical Pacific Ocean GCM betWeen 30W and 30'S with horizontal grid spacing of ic in latitude and 2°in longitude,and with 14 vertical layers.The atmospheric component is a global GCM with low-resolution of 4°in lahtude and 5°in longitude,and tWo layers of equal mass in the verhcal between the surfaCe and 200 hFa.The atmospheric GCM includes comprehensive physical processes.The coupled model is subjected to seasonally-varying cycle.Several coupling experiments,ranging from straight forward coupling without flux correction to one with flux correchon,and to so-called predictor-corrector monthly coupling(PCMC),are conducted tO show the esistence and final controlling of the climate drift in the coupled system.After removing the climate drift with the PCMC SCheme,the coupled model is integrated for more than twenty years.The results show reasonable simulations of the anneal mean and its seasollal cycle of the atmospheric and￣ante circulahon.The model also ProduCeS the coherent intermnual variations of the climate system, manifesting the observed EI Nifio/Southern OSCillation(ENSO).

A parameterization scheme of vertical mixing due to inertial internal wave breaking in the ocean general circulation model

Based on the theoretical spectral model of inertial internal wave breaking （fine structure） proposed previ- ously, in which the effects of the horizontal Coriolis frequency component f-tilde on a potential isopycnal are taken into account, a parameterization scheme of vertical mixing in the stably stratified interior be- low the surface mixed layer in the ocean general circulation model （OGCM） is put forward preliminarily in this paper. Besides turbulence, the impact of sub-mesoscale oceanic processes （including inertial internal wave breaking product） on oceanic interior mixing is emphasized. We suggest that adding the inertial inter- hal wave breaking mixing scheme （F-scheme for short） put forward in this paper to the turbulence mixing scheme of Canuto et al. （T-scheme for short） in the OGCM, except the region from 15°S to 15°N. The numeri- cal results ofF-scheme by usingWOA09 data and an OGCM （LICOM, LASG/IAP climate system ocean model） over the global ocean are given. A notable improvement in the simulation of salinity and temperature over the global ocean is attained by using T-scheme adding F-scheme, especially in the mid- and high-latitude regions in the simulation of the intermediate water and deep water. We conjecture that the inertial internal wave breaking mixing and inertial forcing of wind might be one of important mechanisms maintaining the ventilation process. The modeling strength of the Atlantic meridional overturning circulation （AMOC） by using T-scheme adding F-scheme may be more reasonable than that by using T-scheme alone, though the physical processes need to be further studied, and the overflow parameterization needs to be incorporated. A shortcoming in F-scheme is that in this paper the error of simulated salinity and temperature by using T-scheme adding F-scheme is larger than that by using T-scheme alone in the subsurface layer.