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Profit and loss decomposition in continuous time and approximations

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  • Gero Junike
  • Hauke Stier
  • Marcus C. Christiansen

Abstract

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 It\^o'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.

Suggested Citation

  • Gero Junike & Hauke Stier & Marcus C. Christiansen, 2022. "Profit and loss decomposition in continuous time and approximations," Papers 2212.06733, arXiv.org, revised Dec 2024.
    • Handle: RePEc:arx:papers:2212.06733
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    References listed on IDEAS

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    8. Anthony Shorrocks, 2013. "Decomposition procedures for distributional analysis: a unified framework based on the Shapley value," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 11(1), pages 99-126, March.
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    Cited by:

    1. Marcus C Christiansen, 2023. "Axiomatic characterization of pointwise Shapley decompositions," Papers 2303.07773, arXiv.org.

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