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Time-consistency of cash-subadditive risk measures

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  • Elisa Mastrogiacomo
  • Emanuela Rosazza Gianin

Abstract

The main goal of this paper is to investigate under which conditions cash-subadditive convex dynamic risk measures are time-consistent. Proceeding as in Detlefsen and Scandolo \cite{detlef-scandolo} and inspired by their result, we give a dual representation of dynamic cash-subadditive convex risk measures (that can also be seen as particular case of the dual quasiconvex representation). The main result of the paper consists in providing, in the cash-subadditive case, a sufficient condition for strong time-consistency (or recursivity) in terms of a generalized cocycle condition. On one hand, our result can be seen as an extension to cash-subadditive convex dynamic risk measures of Theorem 2.5 in Bion-Nadal \cite{bion-nadal-FS}; on the other hand, it is weaker since strong time-consistency is not fully characterized. Finally, we exploit the relation between different notions of time-consistency.

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  • Elisa Mastrogiacomo & Emanuela Rosazza Gianin, 2015. "Time-consistency of cash-subadditive risk measures," Papers 1512.03641, arXiv.org.
    • Handle: RePEc:arx:papers:1512.03641
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    References listed on IDEAS

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    9. Freddy Delbaen & Shige Peng & Emanuela Rosazza Gianin, 2010. "Representation of the penalty term of dynamic concave utilities," Finance and Stochastics, Springer, vol. 14(3), pages 449-472, September.
    10. Patrick Cheridito & Freddy Delbaen & Michael Kupper, 2005. "Coherent and convex monetary risk measures for unbounded càdlàg processes," Finance and Stochastics, Springer, vol. 9(3), pages 369-387, July.
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    12. Rosazza Gianin, Emanuela, 2006. "Risk measures via g-expectations," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 19-34, August.
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    Cited by:

    1. Elisa Mastrogiacomo & Emanuela Rosazza Gianin, 2019. "Time-consistency of risk measures: how strong is such a property?," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 287-317, June.
    2. Giulia Di Nunno & Emanuela Rosazza Gianin, 2024. "Cash non-additive risk measures: horizon risk and generalized entropy," Papers 2401.14443, arXiv.org, revised Jun 2024.

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