Stochastics and Finance Seminar: Jan Obloj -- Robust finance. Part I

Speaker: Prof Jan Obloj (Oxford)

Title: Robust finance.  Part I -- proof-of-concept applications using historical time
series and market option prices 

Abstract: In this talk I introduce briefly the robust paradigm which strives to
interpolate the modelling spectrum: from agnostic model-free to classical
model-specific.  It offers methods to walk the spectrum and quantify the impact of
making assumptions and/or using market data.  I explain briefly how classical
fundamental notions and theorems in quantitative finance extend to the robust setting
-- I plan to cover this in more detail in "Part II -- fundamental theorems".  In
this Part I, I mostly focus on simple concrete examples.  I use vanilla option prices,
together with agent-prescribed bounds on key market characteristics, to drive the
interval of no-arbitrage prices and the associated hedging strategies.  The setting can
be seen as a constrained variant of the classical optimal transportation problem and
comes with a natural pricing-hedging duality.  I discuss numerical methods based on
discretisation and LP implementation and on a deep NN optimisation.  I look at ways to
coherently combine option prices data with past time series data, leading to a dynamic
robust risk estimation.  I explain how such non-parametric statistical estimators of key
quantities (e.g., superhedging prices, 10-days V@R) superimposed with option prices can
be treated as information signals.  Based on joint works with Stephan Eckstein, Gaoyue
Guo, Tongseok Lim and Johannes Wiesel.

http://www.maths.usyd.edu.au/u/SemConf/Stochastics_Finance/seminar.html