Mahmoud A. Eissa

In this paper, we discuss an EIQJR model with stochastic perturbation. First, a globally positive solution of the proposed model has been discussed. In addition, the global asymptotic stability and exponential mean-square stability of the disease-free equilibrium have been proven under suitable conditions for our model. This means that the disease will die over time. We investigate the asymptotic behavior around the endemic equilibrium of the deterministic model to show when the disease will prevail. Constructing a suitable Lyapunov functional method is crucial to our investigation. Parameter estimations and numerical simulations are performed to depict the transmission process of COVID-19 pandemic in China and to support analytical results.

Although the concept of symmetry is widely used in many fields, it is almost not discussed in finance. This concept appears to be relevant in relation, for example, to mathematical models that can predict stock prices to contribute to the decision-making process. This work considers the stock price of European options with a new class of the non-constant delay model. The stochastic pantograph differential equation (SPDE) with a variable delay is provided in order to overcome the weaknesses of using stochastic models with constant delay. The proposed model is constructed to improve the evaluation process and prediction accuracy for stock prices. The feasibility of the proposed model is introduced under relatively weak conditions imposed on its volatility function. Furthermore, the sensitivity of time lag is discussed. The robust stochastic theta Milstein (STM) method is combined with the Monte Carlo simulation to compute asset prices within the proposed model. In addition, we prove that the numerical solution can preserve the non-negativity of the solution of the model. Numerical experiments using real financial data indicate that there is an increasing possibility of prediction accuracy for the proposed model with a variable delay compared to non-linear models with constant delay and the classical Black and Scholes model.

Stochastic functional differential equation (SFDE) with constant delay has been used for modelling the price of a firm and European option. However, we can find some weak points such as bounded memory and availability of past event, when using delayed model with constant delay in some applications. Stochastic pantograph differential equation (SPDE) is very special SFDE with variable delay and unbounded memory. In this work, in order to overcome the weaknesses of delayed model with constant delay, we develop a nonlinear delayed model with variable delay for pricing corporate when claim value depends on firm value and time follows a nonlinear SPDE. We proved that, the proposed model is feasible. In addition, a random partial differential equation (RPDE) is derived which satisfied with the corporate claim of value depends on firm value and time. The solution of RPDE is evaluate the debt and equity of a firm. The proposed model with variable delay is more sufficiently flexible to fit real market data, particularly if practitioners are considering the future volatility depends on the past volatility with take into account the variable delay, which can reflect a historical image of volatility more randomly with unbounded memory.

Recently, there has been a growing interest in the production of electricity from renewable energy sources (RES). The RES investment is characterized by uncertainty, which is long-term, costly, depend on feed-in-tariff and support schemes. In this paper, we address the real option valuation (ROV) of a solar power plant investment. The real option framework is investigated. This framework considers the renewable certificate price, furthermore the cost of delay between establishing and operating the solar power plant. The optimal time of launching the project and assess the value of deferred option are discussed. The new three stage numerical methods are constructed, the Lobatto3C-Milstein (L3CM) methods. The numerical methods are integrated with concept of Black-Scholes option pricing theory, and applied in option valuation for solar energy investment with uncertainty. The numerical results of L3CM, finite difference and Monte Carlo methods are compared to show the efficiency of our methods. Our data set refers to the Arab Republic of Egypt.

Recently, there has been a growing interest in the production of electricity from renewable energy sources (RES). The RES investment is characterized by uncertainty, which is long-term, costly and depends on feed-in tariff and support schemes. In this paper, we address the real option valuation (ROV) of a solar power plant investment. The real option framework is investigated. This framework considers the renewable certificate price and, further, the cost of delay between establishing and operating the solar power plant. The optimal time of launching the project and assessing the value of the deferred option are discussed. The new three-stage numerical methods are constructed, the Lobatto3C-Milstein (L3CM) methods. The numerical methods are integrated with the concept of Black–Scholes option pricing theory and applied in option valuation for solar energy investment with uncertainty. The numerical results of the L3CM, finite difference and Monte Carlo methods are compared to show the efficiency of our methods. Our dataset refers to the Arab Republic of Egypt.

The system of ordinary differential equations (ODEs) occurs in many fields of engineering science, particularly in the studies of electrical circuits, vibrations, chemical reactions and so on. In this paper we introduce analog cellular computing for solving ordinary differential equations (ODEs) based on cellular neural networks (CNNs) and study the stability. We apply the CNN to analyze and obtain the approximate solutions of the dynamics of (ODEs). The first system consists of two coupled of non-homogenous linear ordinary differential equations which is the Electrical network obtained from (Kirchhoff's Voltage Law) (Kreyszig, 2005). The second system consists of three coupled of non-homogenous nonlinear ordinary differential equations (Li et al., 2007). The computation based on CNN is advantageous as it provides accurate and ultra-fast solutions of ODEs.