Optimal dynamic regulation of carbon emissions market
研究监管者如何动态分配碳排放配额给企业，企业间可交易配额以最小化成本，通过求解监管者与企业的Stackelberg博弈，得到最优动态分配策略的闭式解，该策略能实现期望减排并保持减排努力和配额价格恒定。
Abstract In this article, 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 minimize 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 nonunique, 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 different penalty functions.