This talk is part of a joint seminar with the EEE Control and Power group. After this talk, there will be a talk by Prof. Richard Vinter: “Concepts, Optimality Conditions and Computational Methods”. See for more details.


Optimal dynamic regulation of carbon emissions market


We deal with optimal dynamic carbon emission regulation of a set of firms. On the one hand, the regulator dynamically allocates emission allowances to each firm. On the other hand, firms face idiosyncratic, as well as common, economic shocks on emissions, and they have linear quadratic abatement costs. Firms can trade allowances so as to minimise total expected costs, which arise from abatement, trading and terminal penalty. Using variational methods, we first exhibit in closed-form the market equilibrium in function of the regulator’s dynamic allocation. We then solve the Stackelberg game between the regulator and the firms. The result is a closed-form expression of the optimal dynamic allocation policies that allow a desired expected emission reduction. The optimal policy is unique in the presence of market impact. In absence of market impact, the optimal policy is non unique, but all the optimal policies share common properties. The optimal policies are fully responsive, and therefore induce a constant abatement effort and a constant price of allowances. Our results are robust to some extensions, like risk aversion of firms or different penalty functions.
We conclude by providing analytical and numerical comparisons of the optimal dynamic policy with three existing policies, namely static allocation, Market Stability Reserve and pure tax mechanisms. This is a joint work with René Aid, Paris Dauphine.


Sara Biagini is Associate Professor at LUISS Rome. Her research interests lie at the intersection of stochastic analysis and mathematical finance, with applications to risk measures, optimal asset allocation and climate finance. She is managing editor of International Journal of Theoretical and Applied Finance and associated editor for Mathematical Finance and Review of Derivatives Reserach. Sara holds a PhD in Applied Mathematics from Scuola Normale Superiore. Prior experience includes visiting positions at Columbia, Princeton, LSE and Paris-Dauphine.