Seminar Event Detail

Financial/Actuarial Mathematics

Date:  Tuesday, November 17, 2015
Location:  1360 East Hall (3:00 PM to 4:00 PM)

Title:  Liquidity, risk measures, and concentration of measure

Abstract:   Expanding on techniques of concentration of measure, we propose a quantitative framework for modeling liquidity risk using convex risk measures. The fundamental objects of study are curves of the form rho(lambda X) lambda ge 0, where rho is a convex risk measure and X a financial position (a random variable), and we call such a curve a emph liquidity profile. For some notable classes of risk measures, especially shortfall risk measures, the shape of a liquidity profile is intimately linked with the tail behavior of the underlying X . We exploit this link to systematically bound liquidity profiles from above by other real functions gamma , deriving tractable necessary and sufficient conditions for concentration inequalities of the form rho( lambda X) le gamma( lambda) for all lambda ge 0. These concentration inequalities admit useful dual representations related to transport-entropy inequalities, and this leads to efficient uniform bounds for liquidity profiles for large classes of X . An interesting question of tensorization of concentration inequalities arises when we seek to bound the liquidity profile of a combination f(X,Y) of two positions X and Y in terms of the two individual liquidity profiles of X and Y. Specializing to law invariant risk measures, we uncover a surprising connection between tensorization and certain time consistency properties known as acceptance and rejection consistency, which leads to some new mathematical results on large deviations and dimension-free concentration of measure.

Files: 3252_UMich-riskmeasures.pdf

Speaker:  Daniel Lacker
Institution:  Brown University

Event Organizer:   Erhan Bayraktar


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