fenchel-moreau theorem

Minimal Representation of Insurance Prices

  • Alois Pichler
  • Alexander Shapiro
    • Categories Convex Optimization, Finance and Economics, Statistics Tags , , ,

    This paper addresses law invariant coherent risk measures and their Kusuoka representations. By elaborating the existence of a minimal representation we show that every Kusuoka representation can be reduced to its minimal representation. Uniqueness — in a sense specified in the paper — of the risk measure’s Kusuoka representation is derived from this initial result. … Read more

    On Kusuoka representation of law invariant risk measures

  • Alexander Shapiro
    • Categories Finance and Economics, Stochastic Programming Tags , , , ,

    In this paper we discuss representations of law invariant coherent risk measures in a form of integrals of the Average Value-at-Risk measures. We show that such integral representation exists iff the dual set of the considered risk measure is generated by one of its elements, and this representation is uniquely defined. On the other hand, … Read more