Viscosity Solutions to Optimal Carbon Policies under Regime-Switching Jump-Diffusion Levy processes

Regime-switching Levy processes integrate jump-diffusions and Markov regime-switchings. When they are coalesced with nonlinear partial differential equations of second order, the technique of viscosity solutions proves critical in the resolution process. However, applications to carbon policies are sparse. This paper frames the carbon policy problem as a non-cooperative differential game between a government entity and a commodity company. In a short lease setting, we structure the emission cap, and we derive the optimal carbon policy in which the main admissible controls are the taxation and extraction rates. Our first contribution is the proof of the existence of an emission cap bound Nash Equilibrium for nonlinear Hamilton Jacobi Isaacs (HJI) equations. In this new carbon framework, we subsequently prove that the value functions of the noncooperative game are unique viscosity solutions of the nonlinear HJI equations. Through a numerical application, we find that the optimal carbon policy must enforce a tax and a cap on the rate of extraction for a successful mitigation of CO2 emissions