论文标题
连续时间和近似值的损益分解
Profit and loss decomposition in continuous time and approximations
论文作者
论文摘要
分析利润和损失的演变和来源的金融机构和保险公司通常仅在离散的报告日期观察风险因素，而忽略了详细的道路。连续的时间分解避免了这种弱点，并使分解在不同的报告网格中保持一致。我们从ITô公式的新扩展版本中构造了大量的连续时间分解，并独特地从精确性，对称性和归一化的公理中识别出优选的分解。事实证明，这种独特的分解是递归沙普利值的随机限制，但随着风险因素数量的增加，它遭受了维数的诅咒。当风险因素几乎没有同时跳跃时，我们会产生近似值，这会打破这种诅咒。
Financial institutions and insurance companies that analyze the evolution and sources of profits and losses often look at risk factors only at discrete reporting dates, ignoring the detailed paths. Continuous-time decompositions avoid this weakness and also make decompositions consistent across different reporting grids. We construct a large class of continuous-time decompositions from a new extended version of Itô's formula and uniquely identify a preferred decomposition from the axioms of exactness, symmetry and normalization. This unique decomposition turns out to be a stochastic limit of recursive Shapley values, but it suffers from a curse of dimensionality as the number of risk factors increases. We develop an approximation that breaks this curse when the risk factors almost surely have no simultaneous jumps.
