估计无套利中的套利：一个例子
Arbitrage in Estimate Nothing: an example
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中文总结 AI 辅助
本文通过一个两期反例，证明Duembgen和Rogers的后验加权定价规则存在套利机会，并说明递归一致性失效。
中文摘要 AI 辅助
我们针对Duembgen和Rogers的《Estimate nothing》中后验加权定价规则的无套利性，给出了一个两期反例。两个物理模型都具有严格正的转移密度，且每个模型都配备了一个等价鞅测度。然而，单个衍生品的混合价格在两个交易日之间从$5/2$确定性地降至$2$。如果这些价格是可交易的，那么做空该衍生品并在一个时期后平仓将产生确定的利润。一个有限状态附录也说明了递归一致性的失效。
英文摘要
We give a two-period counterexample to the absence of arbitrage for the posterior-weighted pricing rule in Estimate nothing by Duembgen and Rogers. Both physical models have strictly positive transition densities, and each model is equipped with an equivalent martingale measure. Nevertheless, the mixed price of a single derivative falls deterministically from $5/2$ to $2$ between two trading dates. If these prices are tradable, shorting the derivative and closing the position one period later yields a certain profit. A finite-state appendix also illustrates the failure of recursive consistency.
