基于帕累托最优风险再分配的紧凑证券市场
Compact Securities Markets for Pareto Optimal Reallocation of Risk
摘要：
证券市场是经济学和金融学研究不确定条件下资源分配的基本理论框架。证券既可以重新分配风险，也可以传播概率信息。完全证券市场--每一种可能的自然状态都包含一种证券--支持帕累托最优风险分配。完全市场与联合概率分布一样，也受到潜在事件数量的指数依赖性的影响。我们研究市场是否可以以与联合分布的贝叶斯网络表示相同的方式进行结构化和“压缩”。我们表明，如果所有代理人的风险中性的独立性与市场结构中编码的独立性一致，那么市场是完全的：风险仍然是帕累托最优分配的，但证券的数量可以呈指数级减少。对于某种类型的代理人的集合，关于马尔可夫独立性的协议足以承认紧凑和操作完全的市场。
英文摘要：
The emph{securities market} is the fundamental theoretical framework in economics and finance for resource allocation under uncertainty. Securities serve both to reallocate risk and to disseminate probabilistic information. emph{Complete} securities markets - which contain one security for every possible state of nature - support Pareto optimal allocations of risk. Complete markets suffer from the same exponential dependence on the number of underlying events as do joint probability distributions. We examine whether markets can be structured and "compacted" in the same manner as Bayesian network representations of joint distributions. We show that, if all agents' risk-neutral independencies agree with the independencies encoded in the market structure, then the market is emph{operationally complete}: risk is still Pareto optimally allocated, yet the number of securities can be exponentially smaller. For collections of agents of a certain type, agreement on Markov independencies is sufficient to admit compact and operationally complete markets.
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