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Cash Sub-additive Risk Measures and Interest Rate Ambiguity

Author

Listed:
  • Nicole EL KAROUI

    (Ecole Polytechnique (France))

  • Claudia RAVANELLI

    (University of Zurich)

Abstract

A new class of risk measures called cash sub-additive risk measures is introduced to assess the risk of future financial, non financial and insurance positions. The debated cash additive axiom is relaxed into the cash sub-additive axiom to preserve the original difference between the numeraire of the current reserve amounts and future positions. Consequently, cash sub-additive risk measures can model stochastic and/or ambiguous interest rates or defaultable contingent claims. Practical examples are presented and in such contexts cash additive risk measures cannot be used. Several representations of the cash sub-additive risk measures are provided. The new risk measures are characterized by penalty functions defined on a set of sub-linear probability measures and can be represented using penalty functions associated with cash additive risk measures defined on some extended spaces. The issue of the optimal risk transfer is studied in the new framework using inf-convolution techniques. Examples of dynamic cash sub-additive risk measures are provided via BSDEs where the generator can locally depend on the level of the cash sub-additive risk measure.

Suggested Citation

  • Nicole EL KAROUI & Claudia RAVANELLI, 2008. "Cash Sub-additive Risk Measures and Interest Rate Ambiguity," Swiss Finance Institute Research Paper Series 08-09, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp0809
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    File URL: http://ssrn.com/abstract=959092
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    Cited by:

    1. Erindi Allaj, 2014. "Risk measuring under liquidity risk," Papers 1412.6745, arXiv.org.
    2. {L}ukasz Delong, 2010. "BSDEs with time-delayed generators of a moving average type with applications to non-monotone preferences," Papers 1008.3722, arXiv.org, revised Jul 2011.

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    More about this item

    Keywords

    Risk measures; Fenchel-Legendre transform; model uncertainty; inf-convolution; backward stochastic di®erential equations.;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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