基于奇异前向后向随机微分方程的多期碳市场模型
Modelling multi-period carbon markets using singular forward backward SDEs
摘要：
我们介绍了一个模型的排放量和排放配额的价格在碳市场，如欧盟排放交易系统（EU ETS）的演变。该模型考虑了多个交易周期或阶段，以及可能发生合规的多个时间。在每个交易期结束时，参与公司必须放弃在该期间的排放配额，额外的配额可用于在随后的时期遵守规定。我们表明，多期津贴定价问题对于连接交易期的各种机制（例如银行业务、借贷和津贴提取）来说都是适当的。结果是基于分析的前向-倒向随机微分方程耦合的前向和后向分量，间断终端条件和前向分量是退化的。我们还引入了一个无限期模型，碳市场的一系列的遵守时间，没有结束日期。我们表明，在适当的条件下，多期定价问题的价值函数收敛，随着期间数的增加，这个无限期模型的价值函数，并且这些功能是唯一的。
英文摘要：
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.
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