论文标题
使用单数向后的SDE对多周期碳市场进行建模
Modelling multi-period carbon markets using singular forward backward SDEs
论文作者
论文摘要
我们介绍了一个模型，用于碳市场（例如欧盟排放贸易体系（EU ETS））中排放量的演变和排放津贴的价格。该模型对多次遵守情况进行了多次交易期或阶段的解释。在每个交易期结束时，参与公司在此期间进行的排放量必须放弃津贴，并且可以在以下时期使用其他津贴来合规。我们表明，对于各种机制（例如银行业，借款和撤回津贴），多个期限的津贴定价问题与交易期相连。结果基于对前向后的随机微分方程的分析，其前向和向后分量，不连续的末端条件和退化的正向组件。我们还引入了一个无限的时期模型，对于一个有一系列合规时间且没有结束日期的碳市场。我们表明，在适当的条件下，随着周期数量的增加，多个周期定价问题的价值函数收敛到该无限周期模型的价值函数，并且此类函数是唯一的。
We introduce a model for the evolution of emissions and the price of emissions allowances in a carbon market such as the European Union Emissions Trading System (EU ETS). The model accounts for multiple trading periods, or phases, with multiple times at which compliance can occur. At the end of each trading period, the participating firms must surrender allowances for their emissions made during that period, and additional allowances can be used for compliance in the following periods. We show that the multi-period allowance pricing problem is well-posed for various mechanisms (such as banking, borrowing and withdrawal of allowances) linking the trading periods. The results are based on the analysis of a forward-backward stochastic differential equation with coupled forward and backward components, a discontinuous terminal condition and a forward component that is degenerate. We also introduce an infinite period model, for a carbon market with a sequence of compliance times and with no end date. We show that, under appropriate conditions, the value function for the multi-period pricing problem converges, as the number of periods increases, to a value function for this infinite period model, and that such functions are unique.
