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Concentration of dynamic risk measures in a Brownian filtration

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  • Tangpi, Ludovic

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.

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  • Tangpi, Ludovic, 2019. "Concentration of dynamic risk measures in a Brownian filtration," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1477-1491.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:5:p:1477-1491
    DOI: 10.1016/j.spa.2018.05.008
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    References listed on IDEAS

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    1. Freddy Delbaen & Shige Peng & Emanuela Rosazza Gianin, 2010. "Representation of the penalty term of dynamic concave utilities," Finance and Stochastics, Springer, vol. 14(3), pages 449-472, September.
    2. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    3. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    4. Rosazza Gianin, Emanuela, 2006. "Risk measures via g-expectations," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 19-34, August.
    5. Daniel Lacker, 2015. "Liquidity, risk measures, and concentration of measure," Papers 1510.07033, arXiv.org, revised Oct 2015.
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    Cited by:

    1. Dai, Yin & Li, Ruinan, 2021. "Transportation cost inequality for backward stochastic differential equations with mean reflection," Statistics & Probability Letters, Elsevier, vol. 177(C).
    2. Tanoue, Yuta, 2024. "Concentration inequality and the weak law of large numbers for the sum of partly negatively dependent φ-subgaussian random variables," Statistics & Probability Letters, Elsevier, vol. 206(C).

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