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UID:calendar.3409.events_uoft_date.0@www.statistics.utoronto.ca
CREATED:20240830T141757Z
DESCRIPTION:\nWhen and Where: \nThursday, March 27, 2025 11:00 am to 12:0
 0 pm \n\nSpeakers \nJan Obłój, University of Oxford \n\nDescription: \nAc
 ross vast array of applications, mathematics is used to build models whic
 h create pathways from inputs to outputs. These models can often be seen a
 s probability measures: discrete (empirical measures over a given data set
 ) or continuous (resulting from an SDE), over finite-dimensional spaces o
 r over pathspaces. The theory of Optimal Transport (OT) offers powerful fu
 lly non-parametric tools to measure distances between probability measures
 , trace geodesics in the space of probability measures, project onto its
  subsets. In this talk, I will survey some recent advancements that lever
 age OT tools and intuition, to describe and manage models, helping with 
 selecting/calibrating models and quantifying model uncertainty. I will use
  questions from mathematical finance as my motivating examples while focus
 ing on providing an overview of the field with its novel mathematical cont
 ributions, including several variants of the classical OT paradigm, and 
 ongoing challenges. In particular, I will discuss robust pricing and hedg
 ing and its link to Martingale-OT, non-parametric calibration via Semimar
 tingale-OT, and Wasserstein distributionally robust optimization and the 
 resulting non-parametric Greeks and risk measurements. I will also mention
  some applications in statistics and machine learning, including adversar
 ial robustness of DNNs. The talk is based on works with many collaborators
 , including: D. Bartl, S. Drapeau, S. Eckstein, G. Guo, I. Guo, Y. J
 iang, B. Joseph, T. Lim, G. Loeper, S. Wang and J. Wiesel.About Jan Ob
 łójJan Obloj is a Professor of Mathematics at the University of Oxford's M
 athematical Institute, an Official Fellow of St John's College Oxford and
  a member of the Oxford-Man Institute of Quantitative Finance. Before comi
 ng to Oxford, he was a Marie Curie Post-Doctoral Fellow at Imperial Colle
 ge London and he holds PhD from University Paris VI and Warsaw University.
  He is the current President of the Bachelier Finance Society and is Fello
 w of the Institute of Mathematical Statistics. He has a general interest i
 n mathematics of randomness. Most of his research sits at the crossroads o
 f various fields, including: probability theory, statistics, mathematic
 al finance, operations research, optimal transportation and data science
 . His main focus is on robustness of the modelling pathways from input out
  outputs, ways to understand and quantify it and his research spans the s
 pectrum from theoretical foundations of robust pricing and hedging paradig
 m in mathematical finance, to practical questions of building fast generi
 c ways to approximate adversarial robustness of deep neural networks. \n\n
 Categories \n Seminar SeriesStatistics Colloquium \n\nAudiences \n Faculty
 Graduate Students
DTSTART;TZID=America/New_York:20250327T110000
DTEND;TZID=America/New_York:20250327T120000
LAST-MODIFIED:20250129T154424Z
SUMMARY:X-OT: on Variants of Optimal Transport Problem and Understanding Mo
 del Robustness
URL;TYPE=URI:https://www.statistics.utoronto.ca/events/x-ot-variants-optima
 l-transport-problem-and-understanding-model-robustness
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