Superhedging and dynamic risk measures under volatility uncertainty

Marcel Nutz, H. Mete Soner

Research output: Contribution to journalArticlepeer-review

41 Scopus citations

Abstract

We consider dynamic sublinear expectations (i.e., time-consistent coherent risk measures) whose scenario sets consist of singular measures corresponding to a general form of volatility uncertainty. We derive a cadlag nonlinear martingale which is also the value process of a superhedging problem. The superhedging strategy is obtained from a representation similar to the optional decomposition. Furthermore, we prove an optional sampling theorem for the nonlinear martingale and characterize it as the solution of a second order backward SDE. The uniqueness of dynamic extensions of static sublinear expectations is also studied.

Original languageEnglish (US)
Pages (from-to)2065-2089
Number of pages25
JournalSIAM Journal on Control and Optimization
Volume50
Issue number4
DOIs
StatePublished - 2012
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics

Keywords

  • G-expectation
  • Nonlinear martingale
  • Replication
  • Risk measure
  • Second order BSDE
  • Superhedging
  • Time consistency
  • Volatility uncertainty

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