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Set-valued risk measures as backward stochastic difference inclusions and equations

Author

Listed:
  • Çağın Ararat

    (Bilkent University)

  • Zachary Feinstein

    (Stevens Institute of Technology)

Abstract

Scalar dynamic risk measures for univariate positions in continuous time are commonly represented via backward stochastic differential equations. In the multivariate setting, dynamic risk measures have been defined and studied as families of set-valued functionals in the recent literature. There are two possible extensions of scalar backward stochastic differential equations for the set-valued framework: (1) backward stochastic differential inclusions, which evaluate the risk dynamics on the selectors of acceptable capital allocations; or (2) set-valued backward stochastic differential equations, which evaluate the risk dynamics on the full set of acceptable capital allocations as a singular object. In this work, the discrete-time setting is investigated with difference inclusions and difference equations in order to provide insights for such differential representations for set-valued dynamic risk measures in continuous time.

Suggested Citation

  • Çağın Ararat & Zachary Feinstein, 2021. "Set-valued risk measures as backward stochastic difference inclusions and equations," Finance and Stochastics, Springer, vol. 25(1), pages 43-76, January.
    • Handle: RePEc:spr:finsto:v:25:y:2021:i:1:d:10.1007_s00780-020-00445-0
    DOI: 10.1007/s00780-020-00445-0
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    More about this item

    Keywords

    Set-valued risk measure; Dynamic risk measure; Difference inclusion; Set-valued difference equation; Time-consistency;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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