2022/12/13 by Gero Junike, Junike, Gero, Hauke Stier +3 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · Psychology · #Algorithm #Applied mathematics #Attribution #Bond #Capital Investment and Risk Analysis #Combinatorics #Computer science #Economics #FOS: Economics and business #Finance #Financial Markets and Investment Strategies #Financial economics #Invariant (physics) #Limit (mathematics) #Mathematical Finance (q-fin.MF) #Mathematical analysis #Mathematical economics #Mathematical optimization #Mathematical physics #Mathematics #Portfolio #Profit (economics) #Psychology #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.2212.06733
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2022/12/13 · openalex created_date 2022/12/27 · openalex updated_date 2026/07/28
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.