CASH SUBADDITIVE RISK MEASURES AND INTEREST RATE AMBIGUITY

By Nicole El Karoui, Claudia Ravanelli. 2007

177 citations recorded by the source corpus.

A new class of risk measures called cash subadditive risk measures is introduced to assess the risk of future financial, nonfinancial, and insurance positions. The debated cash additive axiom is relaxed into the cash subadditive axiom to preserve the original difference between the numéraire of the current reserve amounts and future positions. Consequently, cash subadditive 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 subadditive risk measures are provided. The new risk measures are characterized by penalty functions defined on a set of sublinear 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 subadditive risk measures are provided via BSDEs where the generator can locally depend on the level of the cash subadditive risk measure.

Subfields: Demography, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/700aa1d10f0fd506fda7cb4487edc6f7e9813ce5

Citations in the corpus

• BSDEs with jumps, optimization and applications to dynamic risk measures (2013, unknown): “In the Brownian case, equality (5.64) corresponds to that in [10] and [12].”
• Liquidity risk theory and coherent measures of risk (2008, unknown): “The property of translational subvariance under the addition of cash first appeared in El Karoui and Ravanelli ( forthcoming ) in a different context.”