Uncertain energy model for electricity and gas futures with application in spark-spread option price

Mehrdoust, Farshid; Noorani, Idin; Xu, Wei

doi:10.1007/s10700-022-09386-z

Cited by 28 publications

(4 citation statements)

References 22 publications

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“…Additionally, Yang and Liu [20] proposed parameter estimation for uncertain partial differential equations and applied it to the population of China. Currently, uncertainty theory have found wide applications in reliability analysis [21,22], finance [23,24], natural gas futures pricing [25], epidemic models [26][27][28], uncertain programming [29,30], seepage equation [31], and more.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of uncertain simple pendulum equation ^*

Qiu,

Liu

2024

J. Phys. A: Math. Theor.

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The law of motion of a simple pendulum system is described by an uncertain simple pendulum equation which is a second-order uncertain differential equation driven by Liu process. The stability of a simple pendulum system refers to whether the system tends to the equilibrium state under small perturbation. In order to discuss the sensitivity of the uncertain simple pendulum equation to the perturbation in the initial state, we give the concept of many kinds of stability of the uncertain simple pendulum equation, including almost deterministic stability, distributional stability and exponential stability. And, the sufficient conditions of almost deterministic stability, distributional stability and exponential stability of the uncertain simple pendulum equation are proved respectively.

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Section: Introductionmentioning

confidence: 99%

Stability analysis of uncertain simple pendulum equation ^*

Qiu,

Liu

2024

J. Phys. A: Math. Theor.

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“…For the purpose of avoiding this problem, the residual of uncertain differential equation corresponding to the observed data was defined by Liu and Liu [27], and new methods based on residuals were proposed (Liu and Liu [27], Liu and Liu [25]). Until now, a series of real-world observed data have been modeled by uncertain differential equation, such as cumulative number of COVID-19 infections in China (Lio and Liu [19], Chen et al [20], Jia and Chen [11]), plasma folate concentration (Liu and Yang [29]), noise in circuit system (Liu [24]), noise in chemical reaction (Tang and Yang [8]), Alibaba stock price (Liu and Liu [27]), natural gas prices (Mehrdoust et al [7]), and US Dollar to Chinese Yuan exchange rate (Ye and Liu [13]).…”

Section: Introductionmentioning

confidence: 99%

Modeling China's Per Capita Disposable Income by Uncertain Statistics

Jia,

Tang

2023

Preprint

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Uncertain statistics is a set of mathematical techniques for collecting, analyzing and interpreting data by uncertainty theory. There are mainly three modeling methods in uncertain statistics: uncertain time series analysis, uncertain regression analysis, and uncertain differential equation. This paper applies these tools to modeling China's per capita disposable income, and employs uncertain hypothesis test to determine whether the estimated uncertain statistical models fit China's per capita disposable income. In addition, this paper shows that it is necessary to use uncertain statistics instead of probability statistics to model China's per capita disposable income by investigating the corresponding residuals.

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“…Furthermore, Liu and Liu [17] explored a modified maximum likelihood estimation, and then Liu and Liu [18] introduced the least squares estimation. Over time, uncertain differential equations have found applications across various fields, including currency exchange rate analysis by Ye and Liu [30], natural gas price analysis by Mehrdoust et al [22], electric circuit modeling by Liu [12], pharmacokinetics research by Liu and Yang [20], population dynamics analysis in China by Yang and Liu [23], and epidemic spread as studied by Chen et al [3] and Jia and Chen [4].…”

Section: Introductionmentioning

confidence: 99%

Analysis of EUR to USD Exchange Rates with Uncertain Time Series Model and Uncertain Differential Equation

Hao,

Wu,

2023

Preprint

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As a crucial theory and method to analyze and interpret data in practice by means of uncertainty theory, uncertain statistics is composed of some mathematical tools, and the two most important tools are uncertain time series analysis and uncertain differential equation. For the sake of predicting the future EUR to USD exchange rates, this paper uses the tools of uncertain time series analysis and uncertain differential equation to model the EUR to USD exchange rates from January 2018 to May 2023. Following that, the fitness of the estimated uncertain statistical models to the data set is also verified by using the uncertain hypothesis test. Finally, by means of testing the stochastic hypothesis of the estimated statistical model based on the specific residuals of the EUR to USD exchange rates, the inappropriateness of the stochastic statistical model is also pointed out in this paper.

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Uncertain energy model for electricity and gas futures with application in spark-spread option price

Cited by 28 publications

References 22 publications

Stability analysis of uncertain simple pendulum equation ^*

Stability analysis of uncertain simple pendulum equation ^*

Modeling China's Per Capita Disposable Income by Uncertain Statistics

Analysis of EUR to USD Exchange Rates with Uncertain Time Series Model and Uncertain Differential Equation

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Uncertain energy model for electricity and gas futures with application in spark-spread option price

Cited by 28 publications

References 22 publications

Stability analysis of uncertain simple pendulum equation *

Stability analysis of uncertain simple pendulum equation *

Modeling China's Per Capita Disposable Income by Uncertain Statistics

Analysis of EUR to USD Exchange Rates with Uncertain Time Series Model and Uncertain Differential Equation

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Stability analysis of uncertain simple pendulum equation ^*

Stability analysis of uncertain simple pendulum equation ^*