Time-dynamic evaluations under non-monotone information generated by marked point processes
针对金融和保险中信息受限导致信息动态非单调的情况，将经典鞅表示理论扩展到标记点过程生成的非单调信息，并用量化信息损失效应的对称部分补充了传统仅描述创新的鞅表示，通过寿险和信用风险案例展示结果。
Abstract 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.