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An optimal control model of carbon reduction and trading
1. | Department of Mathematics, Tongji University, Shanghai 200092, China |
References:
[1] |
F. Black and M. Scholes, The pricing of options and corporate liabilities, Journal of Political Economy, 81 (1973), 637-654.
doi: 10.1086/260062. |
[2] |
R. Carmona, M. Fehr and J. Hinz, Optimal stochastic control and carbon price formation, SIAM Journal on Control and Optimization, 48 (2009), 2168-2190.
doi: 10.1137/080736910. |
[3] |
R. Carmona, M. Fehr, J. Hinz and A. Porchet, Market design for emission trading schemes, SIAM Review, 52 (2010), 403-452.
doi: 10.1137/080722813. |
[4] |
B. Commoner, The environmental cost of economic growth, In R.G. Ridker (Ed.), Population, Resources and the Environment, Washington, DC, U.S. Government Printing Office, (1972), 339-363. |
[5] |
E. Commission, The EU emissions trading system (EU ETS),, 2013, ().
|
[6] |
M. G. Crandall and P. L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Transactions of the American Mathematical Society, 277 (1983), 1-42.
doi: 10.1090/S0002-9947-1983-0690039-8. |
[7] |
M. G. Crandall and P. L. Lions, User's guide to viscosity solutions of second order partial differential equations, Bulletin of the American Mathematical Society, 27 (1992), 1-67.
doi: 10.1090/S0273-0979-1992-00266-5. |
[8] |
G. Daskalakis, D. Psychoyios and P. N. Markellos, Modeling CO$_2$ emission allowance prices and derivatives: Evidence from the European trading scheme, Journal of Banking and Finance, 33 (2009), 1230-1241. |
[9] |
T. Dietz and E. A. Rosa, Rethinking the environmental impacts of population, affluence and technology, Human Ecology Review, 1 (1994), 277-300. |
[10] |
W. H. Fleming and H. M. Soner, Controlled Markov Processes and Viscosity Solutions, Springer, New York, 2 edition, 2006. |
[11] |
H. Guo and J. Liang, An optimal control model for reducing and trading of carbon emissions, Physica A: Statistical Mechanics and its Applications, 446 (2016), 11-21, Available from: http://dx.doi.org/10.1016/j.physa.2015.10.076.
doi: 10.1016/j.physa.2015.10.076. |
[12] |
C. Hepburn, Carbon trading: A review of the Kyoto mechanisms, The Annual Review of Environment and Resources, 32 (2007), 375-393.
doi: 10.1146/annurev.energy.32.053006.141203. |
[13] |
R. C. Merton, Theory of rational option pricing, Bell Journal of Economics and Management Sciences, 4 (1973), 141-183.
doi: 10.2307/3003143. |
[14] |
R. C. Merton, Optimum consumption and portfolio rules in a continuous-time model, Journal of Economic Theory, 3 (1971), 373-413.
doi: 10.1016/0022-0531(71)90038-X. |
[15] |
R. C. Merton, Lifetime portfolio selection under uncertainty: The continuous-time case, The Review of Economics and Statistics, 51 (1969), 247-257. |
[16] |
J. Seifert, M. Uhrig-Homburg and M. Wagner, Dynamic behavior of $CO_2$ spot prices, Journal of Environmental Economics and Management, 56 (2008), 180-194. |
[17] |
A. Tsoularis and J. Wallace, Analysis of logistic growth models, Mathematical Biosciences, 179 (2002), 21-55.
doi: 10.1016/S0025-5564(02)00096-2. |
[18] |
M. Wang, M. Wang and S. Wang, Optimal investment and uncertainty on China's carbon emission abatement, Energy Policy, 41 (2012), 871-877.
doi: 10.1016/j.enpol.2011.11.077. |
[19] |
X. Yang and J. Liang, Minimization of the nation cost due to carbon emission, Systems Engineering - Theory and Practice, 34 (2014), 640-647. |
[20] |
X. Yang, Optimal control problems associated with carbon emission abatement and leveraged credit derivatives, Ph. D Thesis, Tongji University, 2015. |
[21] |
E. Zagheni and F. C. Billari, A cost valuation model based on a stochastic representation of the IPAT equation, Population and Environment, 29 (2007), 68-82.
doi: 10.1007/s11111-008-0061-1. |
show all references
References:
[1] |
F. Black and M. Scholes, The pricing of options and corporate liabilities, Journal of Political Economy, 81 (1973), 637-654.
doi: 10.1086/260062. |
[2] |
R. Carmona, M. Fehr and J. Hinz, Optimal stochastic control and carbon price formation, SIAM Journal on Control and Optimization, 48 (2009), 2168-2190.
doi: 10.1137/080736910. |
[3] |
R. Carmona, M. Fehr, J. Hinz and A. Porchet, Market design for emission trading schemes, SIAM Review, 52 (2010), 403-452.
doi: 10.1137/080722813. |
[4] |
B. Commoner, The environmental cost of economic growth, In R.G. Ridker (Ed.), Population, Resources and the Environment, Washington, DC, U.S. Government Printing Office, (1972), 339-363. |
[5] |
E. Commission, The EU emissions trading system (EU ETS),, 2013, ().
|
[6] |
M. G. Crandall and P. L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Transactions of the American Mathematical Society, 277 (1983), 1-42.
doi: 10.1090/S0002-9947-1983-0690039-8. |
[7] |
M. G. Crandall and P. L. Lions, User's guide to viscosity solutions of second order partial differential equations, Bulletin of the American Mathematical Society, 27 (1992), 1-67.
doi: 10.1090/S0273-0979-1992-00266-5. |
[8] |
G. Daskalakis, D. Psychoyios and P. N. Markellos, Modeling CO$_2$ emission allowance prices and derivatives: Evidence from the European trading scheme, Journal of Banking and Finance, 33 (2009), 1230-1241. |
[9] |
T. Dietz and E. A. Rosa, Rethinking the environmental impacts of population, affluence and technology, Human Ecology Review, 1 (1994), 277-300. |
[10] |
W. H. Fleming and H. M. Soner, Controlled Markov Processes and Viscosity Solutions, Springer, New York, 2 edition, 2006. |
[11] |
H. Guo and J. Liang, An optimal control model for reducing and trading of carbon emissions, Physica A: Statistical Mechanics and its Applications, 446 (2016), 11-21, Available from: http://dx.doi.org/10.1016/j.physa.2015.10.076.
doi: 10.1016/j.physa.2015.10.076. |
[12] |
C. Hepburn, Carbon trading: A review of the Kyoto mechanisms, The Annual Review of Environment and Resources, 32 (2007), 375-393.
doi: 10.1146/annurev.energy.32.053006.141203. |
[13] |
R. C. Merton, Theory of rational option pricing, Bell Journal of Economics and Management Sciences, 4 (1973), 141-183.
doi: 10.2307/3003143. |
[14] |
R. C. Merton, Optimum consumption and portfolio rules in a continuous-time model, Journal of Economic Theory, 3 (1971), 373-413.
doi: 10.1016/0022-0531(71)90038-X. |
[15] |
R. C. Merton, Lifetime portfolio selection under uncertainty: The continuous-time case, The Review of Economics and Statistics, 51 (1969), 247-257. |
[16] |
J. Seifert, M. Uhrig-Homburg and M. Wagner, Dynamic behavior of $CO_2$ spot prices, Journal of Environmental Economics and Management, 56 (2008), 180-194. |
[17] |
A. Tsoularis and J. Wallace, Analysis of logistic growth models, Mathematical Biosciences, 179 (2002), 21-55.
doi: 10.1016/S0025-5564(02)00096-2. |
[18] |
M. Wang, M. Wang and S. Wang, Optimal investment and uncertainty on China's carbon emission abatement, Energy Policy, 41 (2012), 871-877.
doi: 10.1016/j.enpol.2011.11.077. |
[19] |
X. Yang and J. Liang, Minimization of the nation cost due to carbon emission, Systems Engineering - Theory and Practice, 34 (2014), 640-647. |
[20] |
X. Yang, Optimal control problems associated with carbon emission abatement and leveraged credit derivatives, Ph. D Thesis, Tongji University, 2015. |
[21] |
E. Zagheni and F. C. Billari, A cost valuation model based on a stochastic representation of the IPAT equation, Population and Environment, 29 (2007), 68-82.
doi: 10.1007/s11111-008-0061-1. |
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