Concentration of dynamic risk measures in a Brownian filtration
Risk Management
2018-05-24 v1 Probability
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.
Keywords
Cite
@article{arxiv.1805.09014,
title = {Concentration of dynamic risk measures in a Brownian filtration},
author = {Ludovic Tangpi},
journal= {arXiv preprint arXiv:1805.09014},
year = {2018}
}