Non-implementability of Arrow–Debreu equilibria by continuous trading under volatility uncertainty
Non-implementability of Arrow–Debreu equilibria by continuous trading under volatility uncertainty
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DOI：
10.1007/s00780-018-0362-x
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发表时间：
2018
影响因子：
1.7
通讯作者：
Patrick Beissner;F. Riedel
中科院分区：
文献类型：
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作者：
Patrick Beissner;F. Riedel
在扩散模型中，一些适当选择的金融证券允许完成市场。因此，静态阿罗-德布鲁均衡的有效配置可以通过动态交易在拉德纳均衡中实现。我们证明，如果波动性存在奈特不确定性，这个著名的结果一般是不成立的。当且仅当均衡分配的贴现净交易在平均值中没有歧义时，存在与阿罗-德布鲁均衡相同的有效配置的Radner均衡。这一属性在禀赋中普遍被违反，因此阿罗-德布鲁均衡分配通常无法通过动态交易一些长期资产来实现。
In diffusion models, a few suitably chosen financial securities allow to complete the market. As a consequence, the efficient allocations of static Arrow–Debreu equilibria can be attained in Radner equilibria by dynamic trading. We show that this celebrated result generically fails if there is Knightian uncertainty about volatility. A Radner equilibrium with the same efficient allocation as in an Arrow–Debreu equilibrium exists if and only if the discounted net trades of the equilibrium allocation display no ambiguity in the mean. This property is violated generically in endowments, and thus Arrow–Debreu equilibrium allocations are generically unattainable by dynamically trading a few long-lived assets.