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The University of Southampton
Mathematical Sciences

CORMSIS Seminar - Distributionally Robust Shortfall Risk Optimization Model and its Approximation, Prof Huifu Xu (Southampton) Seminar

OR Seminar
Time:
14:00 - 16:00
Date:
23 March 2018
Venue:
Room 10037, Lecture Theatre 10B, Building 54, Mathematical Sciences, University of Southampton, Highfield Campus, SO17 1BJ

For more information regarding this seminar, please email Zudi Lu at Z.Lu@southampton.ac.uk .

Event details

Utility-based shortfall risk (SR) measure is proposed by Follmer and Schied (2002) and has received increasing attention over the past few years for its potential to quantify more effectively the risk of large tail losses than conditional value at risk. In this talk, we revisit the subject by considering a situation where the true probability distribution is unknown but it is possible to obtain some partial information through empirical data, subjective judgements or computer simulation to identify a range (ambiguity set) containing or approximating the true probability distribution. We propose a distributionally robust version of the shortfall risk (DRSR) measure where the worst distribution from the ambiguity set is used to evaluate the SR. It is shown that the DRSR is a convex risk measure and under some special circumstance a coherent risk measure. As an application, we consider an optimization problem with the objective of minimizing the DRSR of a random function and investigate numerical tractability of the optimization problem with the ambiguity set being constructed in various ways including moment conditions, phi-divergence, Kantorovich metric and mixture distribution. We demonstrate that under some specific circumstances where the loss function is piecewise linear and convex, the resulting robust optimization problems are numerically tractable. Some approximation schemes for the ambiguity set are proposed for general cases and error bounds are derived under the Kantorovich metric. Quantitative convergence of the optimal values of the approximation problems is consequently established under moderate conditions.Some preliminary numerical test results are reported for the proposed modelling and computational schemes.

Speaker information

Professor Huifu Xu,

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