
-
Previous Article
Disaster relief routing in limited capacity road networks with heterogeneous flows
- JIMO Home
- This Issue
-
Next Article
Optimal investment and dividend payment strategies with debt management and reinsurance
Modeling and computation of energy efficiency management with emission permits trading
1. | Coordinated Innovation Center for Computable Modeling in Management Science, Tianjin University of Finance and Economics, Tianjin 300222, China |
2. | Department of Mathematics and Statistics, Curtin University, Perth, WA6845, Australia |
In this paper, we present an optimal feedback control model to deal with the problem of energy efficiency management. Especially, an emission permits trading scheme is considered in our model, in which the decision maker can trade the emission permits flexibly. We make use of the optimal control theory to derive a Hamilton-Jacobi-Bellman (HJB) equation satisfied by the value function, and then propose an upwind finite difference method to solve it. The stability of this method is demonstrated and the accuracy, as well as the usefulness, is shown by the numerical examples. The optimal management strategies, which maximize the discounted stream of the net revenue, together with the value functions, are obtained. The effects of the emission permits price and other parameters in the established model on the results have been also examined. We find that the influences of emission permits price on net revenue for the economic agents with different initial quotas are quite different. All the results demonstrate that the emission permits trading scheme plays an important role in the energy efficiency management.
References:
[1] |
International Energy Agency, World Energy Outlook 2006, http://www.iea.org/, 2007. Google Scholar |
[2] |
A. Bernard, A. Haurie, M. Vielle and L. Viguier,
A two-level dynamic game of carbon emission trading between Russia, China, and Annex B countries, Journal of Economic Dynamics and Control, 32 (2008), 1830-1856.
doi: 10.1016/j.jedc.2007.07.001. |
[3] |
S. Chang, X. Wang and Z. Wang, Modeling and computation of transboundary industrial pollution with emission permits trading by stochastic differential game, PLoS ONE, 10 (2015), e0138641. Google Scholar |
[4] |
S. Chang and X. Wang, Modelling and computation in the valuation of carbon derivatives with stochastic convenience yields, PLoS ONE, 10 (2015), e0125679.
doi: 10.1371/journal.pone.0125679. |
[5] |
K. Chang, S. Wang and K. Peng, Mean reversion of stochastic convenience yields for CO$_2$ emissions allowances: Empirical evidence from the EU ETS, The Spanish Review of Financial Economics, 11 (2013), 39-45. Google Scholar |
[6] |
C. Cobb and P. Douglas, A Theory of Production, American Economic Review, 8 (1928), 139-165. Google Scholar |
[7] |
G. Daskalakis, D. Psychoyios and R. Markellos, Modeling CO2 emission allowance prices and derivatives: Evidence from the European trading scheme, Journal of Banking&Finance, 33 (2009), 1230-1241. Google Scholar |
[8] |
E. Dockner, S. Jorgensen, N. Long and G. Sorger,
Differential Games in Economics and Management Science Cambridge University Press, 2000. |
[9] |
L. Greening, D. Greene and C. Difiglio,
Energy efficiency and consumption -the rebound effect -a survey, Energy Policy, 28 (2000), 389-401.
doi: 10.1016/S0301-4215(00)00021-5. |
[10] |
S. Hitzemann and M. Uhrig-Homburg, Empirical performance of reduced form models for emission permit prices Working paper Available at SSRN, (2013), 38pp.
doi: 10.2139/ssrn.2297121. |
[11] |
R. Howarth, B. Haddad and B. Paton,
The economics of energy efficiency: Insights from voluntary participation programs, Energy Policy, 28 (2000), 477-486.
doi: 10.1016/S0301-4215(00)00026-4. |
[12] |
J. Hu and S. Wang,
Total-factor energy efficiency of regions in China, Energy Policy, 34 (2006), 3206-3217.
doi: 10.1016/j.enpol.2005.06.015. |
[13] |
A. Jaffe and R. Stavins,
The energy-efficiency gap: What does it mean?, Energy Policy, 22 (1994), 804-810.
doi: 10.1016/0301-4215(94)90138-4. |
[14] |
W. Jin and Z. Zhang, On the mechanism of international technology diffusion for energy technological progress, Working Paper 2015. Available at SSRN: http://ssrn.com/abstract=2584473 Google Scholar |
[15] |
S. Li,
A differential game of transboundary industrial pollution with emission permits trading, Journal of Optimization Theory and Applications, 163 (2014), 642-659.
doi: 10.1007/s10957-013-0384-7. |
[16] |
S. Osher and F. Solomon,
Upwind difference schemes for hyperbolic system of conservation laws, Mathematics of Computation, 38 (1982), 339-374.
doi: 10.1090/S0025-5718-1982-0645656-0. |
[17] |
M. Pandian,
A partial upwind difference scheme for nonlinear parabolic equations, Journal of Computational and Applied Mathematics, 26 (1989), 219-233.
doi: 10.1016/0377-0427(89)90295-1. |
[18] |
M. Patterson, What is energy efficiency? concepts, indicators and methodological issues, Energy efficiency, 24 (1996), 377-390. Google Scholar |
[19] |
U. Risch,
An upwind finite element method for singularly perturbed elliptic problems and local estimates in the $L^{∞}$-norm, Matehmatical Modelling and Numerical Analysis, 24 (1990), 235-264.
doi: 10.1051/m2an/1990240202351. |
[20] |
S. Schurr,
Energy use, technological change, and productive efficiency: An economic-historical interpretation, Annual Review of Energy, 9 (1984), 409-425.
doi: 10.1146/annurev.eg.09.110184.002205. |
[21] |
J. Seifert, M. Uhrig-Homburg and M. Wagner, Dynamic behavior of CO2 spot prices, Journal of Environmental Economics and Management, 56 (2008), 180-194. Google Scholar |
[22] |
J. Strikwerda,
Finite Difference Schemes and Partial Differential Equations Society for Industrial and Applied Mathematics, 2004. |
[23] |
S. Wang, F. Gao and K. Teo,
An upwind finite-difference method for the approximate of viscosity solutions to Hamilton-Jacobi-Bellman equations, IMA Journal of Mathematics Control and Information, 17 (2000), 167-178.
doi: 10.1093/imamci/17.2.167. |
[24] |
E. Worrell, L. Bernstein, J. Roy, L. Price and J. Harnisch,
Industrial energy efficiency and climate change mitigation, Energy Efficiency, 2 (2009), 109-123.
doi: 10.2172/957331. |
[25] |
S. Zhang, X. Wang and A. Shananin,
Modeling and computation of mean field equilibria in producers' game with emission permits trading, Communications in Nonlinear Science and Numerical Simulation, 37 (2016), 238-248.
doi: 10.1016/j.cnsns.2016.01.020. |
show all references
References:
[1] |
International Energy Agency, World Energy Outlook 2006, http://www.iea.org/, 2007. Google Scholar |
[2] |
A. Bernard, A. Haurie, M. Vielle and L. Viguier,
A two-level dynamic game of carbon emission trading between Russia, China, and Annex B countries, Journal of Economic Dynamics and Control, 32 (2008), 1830-1856.
doi: 10.1016/j.jedc.2007.07.001. |
[3] |
S. Chang, X. Wang and Z. Wang, Modeling and computation of transboundary industrial pollution with emission permits trading by stochastic differential game, PLoS ONE, 10 (2015), e0138641. Google Scholar |
[4] |
S. Chang and X. Wang, Modelling and computation in the valuation of carbon derivatives with stochastic convenience yields, PLoS ONE, 10 (2015), e0125679.
doi: 10.1371/journal.pone.0125679. |
[5] |
K. Chang, S. Wang and K. Peng, Mean reversion of stochastic convenience yields for CO$_2$ emissions allowances: Empirical evidence from the EU ETS, The Spanish Review of Financial Economics, 11 (2013), 39-45. Google Scholar |
[6] |
C. Cobb and P. Douglas, A Theory of Production, American Economic Review, 8 (1928), 139-165. Google Scholar |
[7] |
G. Daskalakis, D. Psychoyios and R. Markellos, Modeling CO2 emission allowance prices and derivatives: Evidence from the European trading scheme, Journal of Banking&Finance, 33 (2009), 1230-1241. Google Scholar |
[8] |
E. Dockner, S. Jorgensen, N. Long and G. Sorger,
Differential Games in Economics and Management Science Cambridge University Press, 2000. |
[9] |
L. Greening, D. Greene and C. Difiglio,
Energy efficiency and consumption -the rebound effect -a survey, Energy Policy, 28 (2000), 389-401.
doi: 10.1016/S0301-4215(00)00021-5. |
[10] |
S. Hitzemann and M. Uhrig-Homburg, Empirical performance of reduced form models for emission permit prices Working paper Available at SSRN, (2013), 38pp.
doi: 10.2139/ssrn.2297121. |
[11] |
R. Howarth, B. Haddad and B. Paton,
The economics of energy efficiency: Insights from voluntary participation programs, Energy Policy, 28 (2000), 477-486.
doi: 10.1016/S0301-4215(00)00026-4. |
[12] |
J. Hu and S. Wang,
Total-factor energy efficiency of regions in China, Energy Policy, 34 (2006), 3206-3217.
doi: 10.1016/j.enpol.2005.06.015. |
[13] |
A. Jaffe and R. Stavins,
The energy-efficiency gap: What does it mean?, Energy Policy, 22 (1994), 804-810.
doi: 10.1016/0301-4215(94)90138-4. |
[14] |
W. Jin and Z. Zhang, On the mechanism of international technology diffusion for energy technological progress, Working Paper 2015. Available at SSRN: http://ssrn.com/abstract=2584473 Google Scholar |
[15] |
S. Li,
A differential game of transboundary industrial pollution with emission permits trading, Journal of Optimization Theory and Applications, 163 (2014), 642-659.
doi: 10.1007/s10957-013-0384-7. |
[16] |
S. Osher and F. Solomon,
Upwind difference schemes for hyperbolic system of conservation laws, Mathematics of Computation, 38 (1982), 339-374.
doi: 10.1090/S0025-5718-1982-0645656-0. |
[17] |
M. Pandian,
A partial upwind difference scheme for nonlinear parabolic equations, Journal of Computational and Applied Mathematics, 26 (1989), 219-233.
doi: 10.1016/0377-0427(89)90295-1. |
[18] |
M. Patterson, What is energy efficiency? concepts, indicators and methodological issues, Energy efficiency, 24 (1996), 377-390. Google Scholar |
[19] |
U. Risch,
An upwind finite element method for singularly perturbed elliptic problems and local estimates in the $L^{∞}$-norm, Matehmatical Modelling and Numerical Analysis, 24 (1990), 235-264.
doi: 10.1051/m2an/1990240202351. |
[20] |
S. Schurr,
Energy use, technological change, and productive efficiency: An economic-historical interpretation, Annual Review of Energy, 9 (1984), 409-425.
doi: 10.1146/annurev.eg.09.110184.002205. |
[21] |
J. Seifert, M. Uhrig-Homburg and M. Wagner, Dynamic behavior of CO2 spot prices, Journal of Environmental Economics and Management, 56 (2008), 180-194. Google Scholar |
[22] |
J. Strikwerda,
Finite Difference Schemes and Partial Differential Equations Society for Industrial and Applied Mathematics, 2004. |
[23] |
S. Wang, F. Gao and K. Teo,
An upwind finite-difference method for the approximate of viscosity solutions to Hamilton-Jacobi-Bellman equations, IMA Journal of Mathematics Control and Information, 17 (2000), 167-178.
doi: 10.1093/imamci/17.2.167. |
[24] |
E. Worrell, L. Bernstein, J. Roy, L. Price and J. Harnisch,
Industrial energy efficiency and climate change mitigation, Energy Efficiency, 2 (2009), 109-123.
doi: 10.2172/957331. |
[25] |
S. Zhang, X. Wang and A. Shananin,
Modeling and computation of mean field equilibria in producers' game with emission permits trading, Communications in Nonlinear Science and Numerical Simulation, 37 (2016), 238-248.
doi: 10.1016/j.cnsns.2016.01.020. |






Energy efficiency |
Capital stock |
Value function |
Indigenous innovation |
Absorbed knowledge |
Emission |
0.3 | 0.3 | -0.5658 | 0.1020 | 0.2380 | 0.5320 |
0.5 | -0.3742 | 0.1007 | 0.2350 | 0.5190 | |
0.7 | -0.2476 | 0.0999 | 0.2332 | 0.5112 | |
0.5 | 0.3 | -0.5052 | 0.1116 | 0.1116 | 0.5464 |
0.5 | -0.3201 | 0.1100 | 0.1100 | 0.5320 | |
0.7 | -0.1940 | 0.1090 | 0.1090 | 0.5233 | |
0.7 | 0.3 | -0.4728 | 0.1152 | 0.0494 | 0.5567 |
0.5 | -0.2825 | 0.1134 | 0.0486 | 0.5413 | |
0.7 | -0.1567 | 0.1124 | 0.0482 | 0.5320 |
Energy efficiency |
Capital stock |
Value function |
Indigenous innovation |
Absorbed knowledge |
Emission |
0.3 | 0.3 | -0.5658 | 0.1020 | 0.2380 | 0.5320 |
0.5 | -0.3742 | 0.1007 | 0.2350 | 0.5190 | |
0.7 | -0.2476 | 0.0999 | 0.2332 | 0.5112 | |
0.5 | 0.3 | -0.5052 | 0.1116 | 0.1116 | 0.5464 |
0.5 | -0.3201 | 0.1100 | 0.1100 | 0.5320 | |
0.7 | -0.1940 | 0.1090 | 0.1090 | 0.5233 | |
0.7 | 0.3 | -0.4728 | 0.1152 | 0.0494 | 0.5567 |
0.5 | -0.2825 | 0.1134 | 0.0486 | 0.5413 | |
0.7 | -0.1567 | 0.1124 | 0.0482 | 0.5320 |
[1] |
Arseny Egorov. Morse coding for a Fuchsian group of finite covolume. Journal of Modern Dynamics, 2009, 3 (4) : 637-646. doi: 10.3934/jmd.2009.3.637 |
[2] |
Christopher Bose, Rua Murray. Minimum 'energy' approximations of invariant measures for nonsingular transformations. Discrete & Continuous Dynamical Systems - A, 2006, 14 (3) : 597-615. doi: 10.3934/dcds.2006.14.597 |
[3] |
Y. Latushkin, B. Layton. The optimal gap condition for invariant manifolds. Discrete & Continuous Dynamical Systems - A, 1999, 5 (2) : 233-268. doi: 10.3934/dcds.1999.5.233 |
[4] |
Hakan Özadam, Ferruh Özbudak. A note on negacyclic and cyclic codes of length $p^s$ over a finite field of characteristic $p$. Advances in Mathematics of Communications, 2009, 3 (3) : 265-271. doi: 10.3934/amc.2009.3.265 |
[5] |
Armin Lechleiter, Tobias Rienmüller. Factorization method for the inverse Stokes problem. Inverse Problems & Imaging, 2013, 7 (4) : 1271-1293. doi: 10.3934/ipi.2013.7.1271 |
[6] |
Martin Bohner, Sabrina Streipert. Optimal harvesting policy for the Beverton--Holt model. Mathematical Biosciences & Engineering, 2016, 13 (4) : 673-695. doi: 10.3934/mbe.2016014 |
[7] |
Diana Keller. Optimal control of a linear stochastic Schrödinger equation. Conference Publications, 2013, 2013 (special) : 437-446. doi: 10.3934/proc.2013.2013.437 |
[8] |
Xingchun Wang, Yongjin Wang. Variance-optimal hedging for target volatility options. Journal of Industrial & Management Optimization, 2014, 10 (1) : 207-218. doi: 10.3934/jimo.2014.10.207 |
[9] |
Guido De Philippis, Antonio De Rosa, Jonas Hirsch. The area blow up set for bounded mean curvature submanifolds with respect to elliptic surface energy functionals. Discrete & Continuous Dynamical Systems - A, 2019, 39 (12) : 7031-7056. doi: 10.3934/dcds.2019243 |
[10] |
Tomáš Roubíček. An energy-conserving time-discretisation scheme for poroelastic media with phase-field fracture emitting waves and heat. Discrete & Continuous Dynamical Systems - S, 2017, 10 (4) : 867-893. doi: 10.3934/dcdss.2017044 |
[11] |
Zhi-Min Chen, Philip A. Wilson. Stability of oscillatory gravity wave trains with energy dissipation and Benjamin-Feir instability. Discrete & Continuous Dynamical Systems - B, 2012, 17 (7) : 2329-2341. doi: 10.3934/dcdsb.2012.17.2329 |
[12] |
Qiang Guo, Dong Liang. An adaptive wavelet method and its analysis for parabolic equations. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 327-345. doi: 10.3934/naco.2013.3.327 |
[13] |
Paula A. González-Parra, Sunmi Lee, Leticia Velázquez, Carlos Castillo-Chavez. A note on the use of optimal control on a discrete time model of influenza dynamics. Mathematical Biosciences & Engineering, 2011, 8 (1) : 183-197. doi: 10.3934/mbe.2011.8.183 |
[14] |
Luke Finlay, Vladimir Gaitsgory, Ivan Lebedev. Linear programming solutions of periodic optimization problems: approximation of the optimal control. Journal of Industrial & Management Optimization, 2007, 3 (2) : 399-413. doi: 10.3934/jimo.2007.3.399 |
[15] |
Andrea Cianchi, Adele Ferone. Improving sharp Sobolev type inequalities by optimal remainder gradient norms. Communications on Pure & Applied Analysis, 2012, 11 (3) : 1363-1386. doi: 10.3934/cpaa.2012.11.1363 |
[16] |
Tao Wu, Yu Lei, Jiao Shi, Maoguo Gong. An evolutionary multiobjective method for low-rank and sparse matrix decomposition. Big Data & Information Analytics, 2017, 2 (1) : 23-37. doi: 10.3934/bdia.2017006 |
[17] |
Deren Han, Zehui Jia, Yongzhong Song, David Z. W. Wang. An efficient projection method for nonlinear inverse problems with sparsity constraints. Inverse Problems & Imaging, 2016, 10 (3) : 689-709. doi: 10.3934/ipi.2016017 |
[18] |
Boris Kramer, John R. Singler. A POD projection method for large-scale algebraic Riccati equations. Numerical Algebra, Control & Optimization, 2016, 6 (4) : 413-435. doi: 10.3934/naco.2016018 |
[19] |
Petra Csomós, Hermann Mena. Fourier-splitting method for solving hyperbolic LQR problems. Numerical Algebra, Control & Optimization, 2018, 8 (1) : 17-46. doi: 10.3934/naco.2018002 |
[20] |
Christina Surulescu, Nicolae Surulescu. Modeling and simulation of some cell dispersion problems by a nonparametric method. Mathematical Biosciences & Engineering, 2011, 8 (2) : 263-277. doi: 10.3934/mbe.2011.8.263 |
2019 Impact Factor: 1.366
Tools
Metrics
Other articles
by authors
[Back to Top]