Mean-Square Stability of Milstein Methods for Stochastic Pantograph Equations

Fei-yan, Xiao; Qin, Tingting; Zhang, Chengjian

doi:10.1155/2013/724241

Cited by 4 publications

(1 citation statement)

References 15 publications

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“…On the one hand, the convergence rate is twice as high as in the BIM and, on the other hand, positivity can be achieved without using control functions". In addition, there are are few studies discussing the Milstein-type schemes for SPDE without considering the issue of the positivity of numerical solutions [23]. Therefore, this paper will consider the stochastic theta Milstein (STM) method to numerically solve the SP-SPDE model using real data.…”

Section: Introductionmentioning

confidence: 99%

Improve Stock Price Model-Based Stochastic Pantograph Differential Equation

Eissa

Elsayed

2022

Symmetry

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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.

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Section: Introductionmentioning

confidence: 99%

Improve Stock Price Model-Based Stochastic Pantograph Differential Equation

Eissa

Elsayed

2022

Symmetry

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How diversified fuel‐fired power enterprises keep their competitive advantages to reach sustainable development

Sun

Chen

2018

Env Prog and Sustain Energy

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To decrease carbon emissions, there are three major methods, including developing renewable and clean energy, reducing energy intensity, and decreasing economic growth. However, China has set its economic growth at an annual rate of above 7.2% between 2000 and 2020. Therefore, to achieve the goal of carbon reduction, China will rely more on the development of renewable and clean energy. Conventional fuel‐fired power companies should synthesize economic, political, environmental, and technological factors and implement the most profitable renewable and clean energy projects. To gain a sustainable competitive advantage, diversified projects with persistent profits can theoretically change the industrial structure and the competitive rules. This article studies the relationship between diversification and economic performance. The results show that diversification in conventional fuel‐fired power companies is positively correlated with economic performance. Based on the results, this article proposes a diversification development direction and suggestions. © 2018 American Institute of Chemical Engineers Environ Prog, 38: 137–142, 2019

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Mean-square stability analysis for nonlinear stochastic pantograph equations by transformation approach

Yang

Wang

et al. 2019

Journal of Mathematical Analysis and Applications

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Mean-Square Stability of Milstein Methods for Stochastic Pantograph Equations

Cited by 4 publications

References 15 publications

Improve Stock Price Model-Based Stochastic Pantograph Differential Equation

Improve Stock Price Model-Based Stochastic Pantograph Differential Equation

How diversified fuel‐fired power enterprises keep their competitive advantages to reach sustainable development

Mean-square stability analysis for nonlinear stochastic pantograph equations by transformation approach

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