Minimization of carbon abatement cost: Modeling, analysis and simulation

Xiaoli Yang; Jin Liang; Bei Hu

doi:10.3934/dcdsb.2017158

Article Contents

2017, Volume 22, Issue 7: 2939-2969. Doi: 10.3934/dcdsb.2017158

This issue Previous Article Exponential stability of solutions for retarded stochastic differential equations without dissipativity Next Article Interaction between water and plants: Rich dynamics in a simple model

Minimization of carbon abatement cost: Modeling, analysis and simulation

1.
School of Mathematical Sciences, Tongji University, 1239 Siping Rd, Yangpu Dist, Shanghai 200092, China
2.
Department of Applied Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556, USA

* Corresponding author
* Corresponding author

Received: September 2014

Revised: April 2017

Published online: May 2017

This work is supported by National Natural Science Foundation of China (No. 11271287) and China Scholarship Council. Yang and Liang would like to thank the hospitalities of University of Notre Dame for their visiting where this work is partially carried out.

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Abstract

In this paper, we consider a problem of minimizing the carbon abatement cost of a country. Two models are built within the stochastic optimal control framework based on two types of abatement policies. The corresponding HJB equations are deduced, and the existence and uniqueness of their classical solutions are established by PDE methods. Using parameters in the models obtained from real data, we carried out numerical simulations via semi-implicit method. Then we discussed the properties of the optimal policies and minimal costs. Our results suggest that a country needs to keep a relatively low economy and population growth rate and keep a stable economy in order to reduce the total carbon abatement cost. In the long run, it's better for a country to seek for more efficient carbon abatement techniques and an environmentally friendly way of economic development.

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Mathematics Subject Classification: Primary:35K58, 93E20;Secondary:35K15.

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Figure 1. Plots and ACFs of ln(GDP) and differentiated ln(GDP)

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Figure 2. MAC curve for China and comparison of fitting results

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Figure 7. Relationship between carbon emission, time and minimal cost

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Figure 3. Relationship between $\ln(\epsilon)$ and $\ln{N}$

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Figure 4. Relationship between carbon emission, time and optimal policy

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Figure 5. Relationship between optimal policy and parameters

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Figure 6. Relationship between optimal policy, policy boundary and upper bound

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Figure 8. Relationship between minimal cost and parameters

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Figure 9. Relationship between minimal cost and upper bound for policy

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Figure 10. Relationship between optimal policy and technical parameters

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Figure 11. Relationship between minimal cost and technical parameters

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Table 1. Fitting results: parabolic model VS CRED model

Method m₁ m₂ R²

parabolic 0.0115 0.0162 0.9928

CRED 0.2142 7.6788 0.9342

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