The information dynamics in finance and insurance applications is usually modelled by a filtration. This paper looks at situations where information restrictions apply so that the information dynamics may become non-monotone. A fundamental tool for calculating and managing risks in finance and insurance are martingale representations. We present a general theory that extends classical martingale representations to non-monotone information generated by marked point processes. The central idea is to focus only on those properties that martingales and compensators show on infinitesimally short intervals. While classical martingale representations describe innovations only, our representations have an additional symmetric counterpart that quantifies the effect of information loss. We exemplify the results with examples from life insurance and credit risk.

金融和保险应用中的信息动态通常通过过滤建模。本文着眼于应用信息限制的情况，以便信息动态可能变得非单调。用于计算和管理金融和保险风险的基本工具是鞅表示法。我们提出了一个一般理论，将经典鞅表示扩展到由标记点过程生成的非单调信息。中心思想是只关注鞅和补偿器在无限短的间隔内显示的那些特性。虽然经典鞅表示只描述创新，但我们的表示有一个额外的对称对应物，量化信息丢失的影响。