Fri, 30 Oct 2015

13:00 - 14:00
L6

PhD student talk (On robust pricing--hedging duality in continuous time)

Zhaoxu Hu
((Oxford University)))
Abstract

We pursue robust approach to pricing and hedging in mathematical finance. We consider a continuous time setting in which some underlying assets and options, with continuous paths, are available for dynamic trading and a further set of European options, possibly with varying maturities, is available for static trading. Motivated by the notion of prediction set in Mykland [03], we include in our setup modelling beliefs by allowing to specify a set of paths to be considered, e.g. super-replication of a contingent claim is required only for paths falling in the given set. Our framework thus interpolates between model--independent and model--specific settings and allows to quantify the impact of making assumptions or gaining information. We obtain a general pricing-hedging duality result: the infimum over superhedging prices is equal to supremum over calibrated martingale measures. In presence of non-trivial beliefs, the equality is between limiting values of perturbed problems. In particular, our results include the martingale optimal transport duality of Dolinsky and Soner [13] and extend it to multiple dimensions and multiple maturities.

Thu, 13 Nov 2014
11:00
C5

Convergence properties in Stone spaces

Robert Leek
((Oxford University)))
Abstract

In this talk, I will introduce an internal, structural 
characterisation of certain convergence properties (Fréchet-Urysohn, or 
more generally, radiality) and apply this structure to understand when 
Stone spaces have these properties. This work can be generalised to 
certain Zariski topologies and perhaps to larger classes of spaces 
obtained from other structures.

Wed, 24 Apr 2013
11:30
Queen's College

Boy's surface

David Hume
((Oxford University)))
Abstract

Following the recent paper of Ogasa, we attempt to construct Boy's surface using only paper and tape. If this is successful we hope to address such questions as:

Is that really Boy's surface?

Why should we care?

Do we have any more biscuits?

Wed, 17 Oct 2012
11:00

Rank gradient in Vienna (or what I learnt in the summer)

Alejandra Garrido Angulo -- St Hugh's, 80WR18
((Oxford University)))
Abstract

I will give a brief report on some the topics discussed at the workshop "Golod-Shafarevich groups and rank gradient" that took place this August in Vienna. I will focus on results involving rank gradient.

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