论文标题
有限剂平衡的强烈收敛到平均场极限
Strong Convergence to the Mean-Field Limit of A Finite Agent Equilibrium
论文作者
论文摘要
我们研究了证券市场的基于均衡的持续资产定价问题。在先前的工作[16]中，我们已经表明，有条件的McKean-Vlasov类型的向前向后随机微分方程给出了一定的价格过程，该方程在较大的人口限制下渐近地清除了市场。在当前的工作中，在适当的条件下，我们显示了有限剂平衡的存在及其与[16]中给出的相应平均场限制的强大收敛。作为重要的副产品，我们对两个市场之间平衡价格的差异进行了直接估计。一种由有限种群大小的异质药物和无限种群大小的同质剂组成。
We study an equilibrium-based continuous asset pricing problem for the securities market. In the previous work [16], we have shown that a certain price process, which is given by the solution to a forward backward stochastic differential equation of conditional McKean-Vlasov type, asymptotically clears the market in the large population limit. In the current work, under suitable conditions, we show the existence of a finite agent equilibrium and its strong convergence to the corresponding mean-field limit given in [16]. As an important byproduct, we get the direct estimate on the difference of the equilibrium price between the two markets; one consisting of heterogeneous agents of finite population size and the other of homogeneous agents of infinite population size.
