2018/05/23 by Ludovic Tangpi, Tangpi, Ludovic
Economics, Econometrics and Finance · Decision Sciences · #Stochastic processes and financial applications #Risk and Portfolio Optimization #Financial Risk and Volatility Modeling
paper · pdf · doi:10.48550/arxiv.1805.09014
Motivated by liquidity risk in mathematical finance, D. Lacker 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.