Convex risk measures for càdlàg processes on Orlicz hearts

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Abstract

Our purpose is to study properties and representations of convex risk measures for possibly unbounded càdlàg processes. As the underlying space on which we define convex risk measures we consider spaces of càdlàg processes whose supremum belongs to an Orlicz heart. In order to obtain concrete representations for such convex risk measures, we shall investigate representations of continuous linear functionals on the underlying space. Moreover, many examples of risk measures are introduced. In particular, we deal with risk measures associated with hedging and pricing problems for American claims. Among others, we look into shortfall risk measure in detail.

Original languageEnglish
Pages (from-to)609-625
Number of pages17
JournalSIAM Journal on Financial Mathematics
Volume5
Issue number1
DOIs
Publication statusPublished - 2014 Jan 1

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Keywords

  • American claim
  • Convex risk measure
  • Orlicz heart
  • Randomized stopping time
  • Shortfall risk

ASJC Scopus subject areas

  • Numerical Analysis
  • Finance
  • Applied Mathematics

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