Concentration of dynamic risk measures in a Brownian filtration

Ludovic Tangpi

doi:10.1016/j.spa.2018.05.008

Concentration of dynamic risk measures in a Brownian filtration

Ludovic Tangpi

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1477-1491
Number of pages	15
Journal	Stochastic Processes and their Applications
Volume	129
Issue number	5
DOIs	https://doi.org/10.1016/j.spa.2018.05.008
State	Published - May 2019
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
Modeling and Simulation
Applied Mathematics

Keywords

Backward stochastic differential equations
Brownian filtration
Concentration inequalities
Dynamic risk measures
Superquadratic growth
Transportation inequalities

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10.1016/j.spa.2018.05.008

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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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AU - Tangpi, Ludovic

PY - 2019/5

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AB - 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.

KW - Backward stochastic differential equations

KW - Brownian filtration

KW - Concentration inequalities

KW - Dynamic risk measures

KW - Superquadratic growth

KW - Transportation inequalities

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SP - 1477

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JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 5

ER -

Concentration of dynamic risk measures in a Brownian filtration

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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