## On the impact of tax uncertainty into carbon abatement technology: a stochastic control approach

We formulate a stochastic control problem in continuous time to study the implications of uncertainty in carbon taxes to emissions abatement. We consider a framework where a profit-maximizing electricity producer pays emission taxes and has the option to invest in emission abatement technology. The tax rate is stochastic and may change at random times, for instance in reaction to exogenous events. We assume that the producer chooses the rate of investments in the abatement technology, which are divisible, irreversible and subject to transaction costs. In mathematical terms this corresponds to study a stochastic control problem with constraints where the investment rate is the control variable. We characterize the value function as unique viscosity solution of the associated HJB equation, and provide conditions under which a classical solution exists. We extend the study to the case where taxes are uncertain, but not necessarily random. In this case the producer determines both the optimal production and the optimal investment as the equilibrium strategy of a stochastic differential game with a malevolent opponent (i.e. nature). We prove the existence of the equilibrium by studying the Bellman-Isaacs equation corresponding to the differential game.

Area: CS6 - Stochastic optimal control, BSDEs, and applications (Fulvia Confortola and Alessandro Calvia)

Keywords: Stochastic control, Jump diffusion processes, Stochastic games

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