Concentration of dynamic risk measures in a Brownian filtration

Ludovic Tangpi

Stochastic Processes and their Applications, 2019, vol. 129, issue 5, 1477-1491

Abstract: 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.

Keywords: Dynamic risk measures; Backward stochastic differential equations; Brownian filtration; Superquadratic growth; Concentration inequalities; Transportation inequalities (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2018.05.008

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