An example of a stochastic equilibrium with incomplete markets
An example of a stochastic equilibrium with incomplete markets
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不完全市场随机均衡的一个例子
DOI：
10.1007/s00780-011-0161-0
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发表时间：
2009
影响因子：
1.7
通讯作者：
Gordan Zitkovic
中科院分区：
文献类型：
--
作者：
Gordan Zitkovic
证明了一类不完全连续时间金融环境中随机均衡的存在唯一性，其中市场参与者是具有异类风险厌恶系数的指数效用最大化者，且具有一般的马尔可夫随机天赋。我们设定的不完备性--其来源可以被认为是信用事件或灾难--是真实的，因为不仅价格，而且可复制的债权家族本身也被确定为均衡的一部分。因此，均衡分配不一定是帕累托最优的，相关的代表-代理技术也不能使用。取而代之的是，我们基于一类半线性偏微分方程解的新的稳定性结果而遵循一条新的路线，该偏微分方程解与代理效用最大化问题的Hamilton-Jacobi-Bellman方程有关。这种方法导致了问题的重新表述，其中Banach不动点定理不仅可以用来证明存在唯一性，而且还可以为它的计算提供一个简单而有效的数值过程。
We prove existence and uniqueness of stochastic equilibria in a class of incomplete continuous-time financial environments where the market participants are exponential utility maximizers with heterogeneous risk-aversion coefficients and general Markovian random endowments. The incompleteness featured in our setting—the source of which can be thought of as a credit event or a catastrophe—is genuine in the sense that not only the prices, but also the family of replicable claims itself are determined as a part of the equilibrium. Consequently, equilibrium allocations are not necessarily Pareto optimal and the related representative-agent techniques cannot be used. Instead, we follow a novel route based on new stability results for a class of semilinear partial differential equations related to the Hamilton–Jacobi–Bellman equation for the agents’ utility maximization problems. This approach leads to a reformulation of the problem where the Banach fixed-point theorem can be used not only to show existence and uniqueness, but also to provide a simple and efficient numerical procedure for its computation.