Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/330649 
Year of Publication: 
2025
Citation: 
[Journal:] Finance and Stochastics [ISSN:] 1432-1122 [Volume:] 29 [Issue:] 4 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2025 [Pages:] 1075-1107
Publisher: 
Springer, Berlin, Heidelberg
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.
Subjects: 
Profit and loss attribution
Sequential decompositions
Change analysis
Risk decomposition
Itô’s formula
JEL: 
C02
C30
C63
G10
G12
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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