英文标题：
《A martingale concept for non-monotone information in a jump process
framework》
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作者：
Marcus C. Christiansen
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最新提交年份：
2021
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英文摘要：
The information dynamics in finance and insurance applications is usually modeled by a filtration. This paper looks at situations where information restrictions apply such 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.
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中文摘要：
金融和保险应用中的信息动态通常通过过滤进行建模。本文着眼于信息限制的应用情况，以便信息动态可能变得非单调。计算和管理金融和保险风险的一个基本工具是鞅表示。我们提出了一个将经典鞅表示推广到由标记点过程生成的非单调信息的一般理论。中心思想是只关注鞅和补偿器在无穷短区间上显示的那些性质。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项，用于量化信息丢失的影响。我们用人寿保险和信用风险的例子来举例说明结果。
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分类信息：

一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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