Invited talk: Sara Biagini

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. Optimal policies are not unique but share common properties, which rigorously confirm economic intuition. 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 joint work with René Aid, Dauphine Paris.