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# An optimal control model of carbon reduction and trading

• In this study, a stochastic control model is established for a country to formulate a carbon abatement policy to minimize the total carbon reduction costs. Under Merton's consumption framework, by considering carbon trading, carbon abatement and penalties in a synthetic manner, the model is converted into a two-dimensional Hamilton--Jacobi--Bellman equation. We rigorously prove the existence and uniqueness of its viscosity solution. We also present the numerical results and discuss the properties of the optimal carbon reduction policy and the minimum total costs.
Mathematics Subject Classification: 93E20, 49L25, 35K58.

 Citation:

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