Concentration of dynamic risk measures in a Brownian filtration

Ludovic Tangpi

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arXiv · 1805.09014

Concentration of dynamic risk measures in a Brownian filtration

Ludovic Tangpi

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Abstract

Motivated by liquidity risk in mathematical finance, D. Lacker introduced concentration inequalities for risk measures, i.e. upper bounds on the \emph{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.

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Ludovic Tangpi. 2018-05-23. Concentration of dynamic risk measures in a Brownian filtration. https://arxiv.org/abs/1805.09014

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