Profit and loss decomposition in continuous time and approximations
针对金融机构在离散报告期分析损益来源的缺陷，构建了一类连续时间分解方法，并基于精确性、对称性和归一化公理唯一确定最优分解，同时提出一种近似方法以克服高维风险因素带来的维度诅咒。
Abstract Financial institutions and insurance companies that analyse 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 rearranged version of Itô’s formula, and uniquely identify a preferred decomposition from the axioms of exactness, symmetry and normalisation. 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.