Lobatto-Milstein Numerical Method in Application of Uncertainty Investment of Solar Power Projects

Eissa, Mahmoud A.; Tian, Bo

doi:10.20944/preprints201608.0075.v1

Cited by 2 publications

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“…In this paper, Theorem 7 extended the same results with free parameter , which can be greater than 1. In addition, Corollary 8 proved that for ≥ 3/2, the DSS M methods can preserve the asymptomatic MS stability of the exact solution for SDEs (2) with no restriction on parameters and step-size.…”

Section: Corollary 8 If ≥ 3/2 Then the Dss M Methodsmentioning

confidence: 99%

“…(2), we can see that these methods are not A-stable, and the MS stability conditions of these methods have some restriction on parameters and stepsize. In this section, we discuss the MS stability of new general split-step numerical methods, the DSS M methods ( (5)- (6)) for scalar linear SDEs (2). First, we recall some notations of stability.…”

Section: Notations and Preliminariesmentioning

confidence: 99%

“…In order to describe the properties of SDEs systems, numerical solutions have attracted a lot of attention. There is an extensive literature concerned with explicit and implicit numerical methods for SDEs (see [1][2][3][4][5][6][7]). …”

Section: Introductionmentioning

confidence: 99%

“…Saito and Mitsui [10] proposed the concept of the MS stability for a numerical methods solving (2). The MS stability of the classes of theta methods for scalar SDEs (2) is introduced in [11].…”

Section: Introductionmentioning

confidence: 99%

“…The MS stability of the classes of theta methods for scalar SDEs (2) is introduced in [11]. Higham [9] introduced allowing > 1 in the semiimplicit Milstein scheme benefits in terms of the stability for (2). In literature, there are several attempts to constructing numerical methods based on split-step techniques to improve the fundamental analysis that contains convergence and stability for SDEs.…”

Section: Introductionmentioning

confidence: 99%

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Mean-Square Stability of Split-Step Theta Milstein Methods for Stochastic Differential Equations

Eissa

Zhang

Xiao

2018

Mathematical Problems in Engineering

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The fundamental analysis of numerical methods for stochastic differential equations (SDEs) has been improved by constructing new split-step numerical methods. In this paper, we are interested in studying the mean-square (MS) stability of the new general drifting split-step theta Milstein (DSS M) methods for SDEs. First, we consider scalar linear SDEs. The stability function of the DSS M methods is investigated. Furthermore, the stability regions of the DSS M methods are compared with those of test equation, and it is proved that the methods with ≥ 3/2 are stochastically A-stable. Second, the nonlinear stability of DSS M methods is studied. Under a coupled condition on the drifting and diffusion coefficients, it is proved that the methods with > 1/2 can preserve the MS stability of the SDEs with no restriction on the step-size. Finally, numerical examples are given to examine the accuracy of the proposed methods under the stability conditions in approximation of SDEs.

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Section: Corollary 8 If ≥ 3/2 Then the Dss M Methodsmentioning

confidence: 99%

Section: Notations and Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Mean-Square Stability of Split-Step Theta Milstein Methods for Stochastic Differential Equations

Eissa

Zhang

Xiao

2018

Mathematical Problems in Engineering

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Multi-stage compound real options valuation in residential PV-Battery investment

Swandi

Chapman

et al. 2020

Energy

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Strategic valuation of efficient and well-timed network investments under uncertain electricity market environment has become increasingly challenging, because there generally exist multiple interacting options in these investments, and failing to systematically consider these options can lead to decisions that undervalue the investment. In our work, a real options valuation (ROV) framework is proposed to determine the optimal strategy for executing multiple interacting options within a distribution network investment, to mitigate the risk of financial losses in the presence of future uncertainties. To demonstrate the characteristics of the proposed framework, we determine the optimal strategy to economically justify the investment in residential PV-battery systems for additional grid supply during peak demand periods. The options to defer, and then expand, are considered as multi-stage compound options, since the option to expand is a subsequent option of the former. These options are valued via the least squares Monte Carlo method, incorporating uncertainty over growing power demand, varying diesel fuel price, and the declining cost of PV-battery technology as random variables. Finally, a sensitivity analysis is performed to demonstrate how the proposed framework responds to uncertain events. The proposed framework shows that executing the interacting options at the optimal timing increases the investment value.

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Lobatto-Milstein Numerical Method in Application of Uncertainty Investment of Solar Power Projects

Cited by 2 publications

References 0 publications

Mean-Square Stability of Split-Step Theta Milstein Methods for Stochastic Differential Equations

Mean-Square Stability of Split-Step Theta Milstein Methods for Stochastic Differential Equations

Multi-stage compound real options valuation in residential PV-Battery investment

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