英文标题：
《Election Predictions as Martingales: An Arbitrage Approach》
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作者：
Nassim Nicholas Taleb
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最新提交年份：
2019
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英文摘要：
  We consider the estimation of binary election outcomes as martingales and propose an arbitrage pricing when one continuously updates estimates. We argue that the estimator needs to be priced as a binary option as the arbitrage valuation minimizes the conventionally used Brier score for tracking the accuracy of probability assessors.   We create a dual martingale process $Y$, in $[L,H]$ from the standard arithmetic Brownian motion, $X$ in $(-\\infty, \\infty)$ and price elections accordingly. The dual process $Y$ can represent the numerical votes needed for success.   We show the relationship between the volatility of the estimator in relation to that of the underlying variable. When there is a high uncertainty about the final outcome, 1) the arbitrage value of the binary gets closer to 50\\%, 2) the estimate should not undergo large changes even if polls or other bases show significant variations.   There are arbitrage relationships between 1) the binary value, 2) the estimation of $Y$, 3) the volatility of the estimation of $Y$ over the remaining time to expiration. We note that these arbitrage relationships were often violated by the various forecasting groups in the U.S. presidential elections of 2016, as well as the notion that all intermediate assessments of the success of a candidate need to be considered, not just the final one.
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中文摘要：
我们将二元选举结果的估计视为鞅，并提出了一种当连续更新估计时的套利定价。我们认为，估值器需要作为二元期权定价，因为套利估值最小化了传统上用于跟踪概率评估师准确性的Brier分数。我们从标准的算术布朗运动中创建了一个双鞅过程$Y$，单位为$[L，H]$，$X$（-\\infty，infty）$，并相应地进行了价格选择。双过程$Y$可以代表成功所需的数字投票。我们展示了估计量的波动率与基础变量的波动率之间的关系。当最终结果存在高度不确定性时，1）二进制的套利价值接近50%，2）即使民意调查或其他基础显示出显著变化，估计也不应发生大的变化。1）二元价值，2）Y$美元估值，3）Y$估值在剩余到期时间内的波动性之间存在套利关系。我们注意到，在2016年美国总统选举中，各种预测小组经常违反这些套利关系，以及需要考虑对候选人成功的所有中间评估，而不仅仅是最终评估的概念。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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一级分类：Physics        物理学
二级分类：Physics and Society        物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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