Journal of Risk Model Validation

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Nonconvex noncash risk measures

Chang Cong and Peibiao Zhao

  • The nonweak cone-type acceptable sets with p-norm (1 ≤ p ≤ ∞) are proposed to evaluate the corresponding risk measure.
  • A convex extension of the nonconvex noncash risk measure with p-norm is given associated with the nonweak cone-type acceptable sets.
  • A representation theorem of the nonconvex noncash risk measures is achieved.

In 2018, Cong and Zhao introduced noncash risk measures with 1-norm for weak cone-type acceptable sets. In the present paper, we take a further look at nonconvex, noncash risk measures with p-norm (1 ≤ p ≤ ∞) for nonweak cone-type acceptable sets. A convex extension of the nonconvex, noncash risk measures is given and a representation theorem of a convex extension of the nonconvex, noncash risk measures is achieved.

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