Concentration of dynamic risk measures in a Brownian filtration

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Motivated by liquidity risk in mathematical finance, Lacker (2015) introduced concentration inequalities for risk measures, i.e. upper bounds on the liquidity risk profile of a financial loss. We derive these inequalities in the case of time-consistent dynamic risk measures when the filtration is assumed to carry a Brownian motion. The theory of backward stochastic differential equations (BSDEs) and their dual formulation plays a crucial role in our analysis. Natural by-products of concentration of risk measures are a description of the tail behavior of the financial loss and transport-type inequalities in terms of the generator of the BSDE, which in the present case can grow arbitrarily fast.

Original languageEnglish (US)
Pages (from-to)1477-1491
Number of pages15
JournalStochastic Processes and their Applications
Issue number5
StatePublished - May 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


  • Backward stochastic differential equations
  • Brownian filtration
  • Concentration inequalities
  • Dynamic risk measures
  • Superquadratic growth
  • Transportation inequalities


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