We analyse the structure of local martingale deflators projected on smaller filtrations. In a general continuous-path setting, we show that the local martingale parts in the multiplicative Doob–Meyer decomposition of projected local martingale deflators are themselves local martingale deflators in the smaller information market. Via use of a Bayesian filtering approach, we demonstrate the exact mechanism of how updates on the possible class of models under less information result in the strict supermartingale property of projections of such deflators. Finally, we demonstrate that these projections are unable to span all possible local martingale deflators in the smaller information market, by investigating a situation where market completeness is not retained under filtration shrinkage.

我们分析了预计在较小过滤条件下使用的本地mar充气机的结构。在一般的连续路径设置中，我们表明，在投影的局部mar压缩器的乘法Doob–Meyer分解中，局部mar自身在较小的信息市场中本身就是局部mar。通过使用贝叶斯滤波方法，我们演示了在更少的信息下对可能的模型类别进行更新如何导致此类放气机的投影具有严格的超级martingale属性的精确机制。最后，通过调查在过滤收缩情况下无法保持市场完整性的情况，我们证明了这些预测无法覆盖较小信息市场中所有可能的本地mar生产商。