论文标题
从贝叶斯人的角度套利
Arbitrage from a Bayesian's Perspective
论文作者
论文摘要
本文建立了一个互动信念层次结构的模型，以得出判断套利机会要求贝叶斯市场参与者行使其高阶信念的条件。作为贝叶斯人，代理商必须对未来的资产支出的不确定性，其他市场参与者采用的策略进行全面递归，这些策略是价格汇总的，其他市场参与者对代理商策略的信念，其他市场参与者对代理商认为其策略的信念以及对Ad Infinitum的信念。定义这个无限的先验递归（可以说是层次结构），以及它们如何更新提供了贝叶斯决策问题，等同于该问题的标准资产定价表达。本文的主要结果表明，只有当代理商更新他对其他市场参与者使用的策略和信念的先验递归时，才会出现套利交易。因此，本文通过确定从市场套利到市场参与者信念层次结构的桥梁来将财务基础与游戏理论的基础联系起来。
This paper builds a model of interactive belief hierarchies to derive the conditions under which judging an arbitrage opportunity requires Bayesian market participants to exercise their higher-order beliefs. As a Bayesian, an agent must carry a complete recursion of priors over the uncertainty about future asset payouts, the strategies employed by other market participants that are aggregated in the price, other market participants' beliefs about the agent's strategy, other market participants beliefs about what the agent believes their strategies to be, and so on ad infinitum. Defining this infinite recursion of priors -- the belief hierarchy so to speak -- along with how they update gives the Bayesian decision problem equivalent to the standard asset pricing formulation of the question. The main results of the paper show that an arbitrage trade arises only when an agent updates his recursion of priors about the strategies and beliefs employed by other market participants. The paper thus connects the foundations of finance to the foundations of game theory by identifying a bridge from market arbitrage to market participant belief hierarchies.
