Tight Approximations of Dynamic Risk Measures

Academic Article

Abstract

  • This paper compares two frameworks for measuring risk in a multiperiod setting. The first corresponds to applying a single coherent risk measure to the cumulative future costs, and the second involves applying a composition of one-step coherent risk mappings. We characterize several necessary and sufficient conditions under which one measurement always dominates the other and introduce a metric to quantify how close the two measures are. Using this notion, we address the question of how tightly a given coherent measure can be approximated by lower or upper bounding compositional measures. We exhibit an interesting asymmetry between the two cases: the tightest upper bound can be exactly characterized and corresponds to a popular construction in the literature, whereas the tightest lower bound is not readily available. We show that testing domination and computing the approximation factors are generally NP-hard, even when the risk measures are comonotonic and law-invariant. However, we characterize conditio...
  • Authors

  • Iancu, Dan A
  • Petrik, Marek
  • Subramanian, Dharmashankar
  • Status

    Publication Date

  • August 2015
  • Has Subject Area

    Published In

    Digital Object Identifier (doi)

    Start Page

  • 655
  • End Page

  • 682
  • Volume

  • 40
  • Issue

  • 3