Mathematical Finance Internal Seminar
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Thu, 19/01/2012 13:00 |
Martin Gould |
Mathematical Finance Internal Seminar  |
DH 1st floor SR |
| In recent years, limit order books have been adopted as the pricing mechanism in more than half of the world's financial markets. Thanks to recent technological advances, traders around the globe also now have real-time access to limit order book trading platforms and can develop trading strategies that make use of this "ultimate microscopic level of description". In this talk I will briefly describe the limit order book trade-matching mechanism, and explain how the extra flexibility it provides has vastly impacted the problem of how a market participant should optimally behave in a given set of circumstances. I will then discuss the findings from my recent statistical analysis of real limit order book data for spot trades of 3 highly liquid currency pairs (namely, EUR/USD, GBP/USD, and EUR/GBP) on a large electronic trading platform during May and June 2010, and discuss how a number of my findings highlight weaknesses in current models of limit order books. | |||
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Thu, 26/01/2012 13:00 |
Christoph Reisinger |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| In this seminar, we discuss three questions related to the finite difference computation of early exercise options, one of which has a useful answer, one an interesting one, and one is open. We begin by showing that a simple iteration of the exercise strategy of a finite difference solution is efficient for practical applications and its convergence can be described very precisely. It is somewhat surprising that the method is largely unknown. We move on to discuss properties of a so-called penalty method. Here we show by means of numerical experiments and matched asymptotic expansions that the approximation of the value function has a very intricate local structure, which is lost in functional analytic error estimates, which are also derived. Finally, we describe a gap in the analysis of the grid convergence of finite difference approximations compared to empirical evidence. This is joint work with Jan Witte and Sam Howison. | |||
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Thu, 02/02/2012 13:00 |
Sam Cohen |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| Decision making in the presence of uncertainty is a mathematically delicate topic. In this talk, we consider coherent sublinear expectations on a measurable space, without assuming the existence of a dominating probability measure. By considering discrete-time `martingale' processes, we show that the classical results of martingale convergence and the up/downcrossing inqualities hold in a `quasi-sure' sense. We also give conditions, for a general filtration, under which an `aggregation' property holds, generalising an approach of Soner, Touzi and Zhang (2011). From this, we extend various results on the representation of conditional sublinear expectations to general filtrations under uncertainty. | |||
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Thu, 09/02/2012 13:00 |
various |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
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Thu, 16/02/2012 13:00 |
Gechun Liang |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
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Thu, 23/02/2012 13:00 |
Sergey Shahverdyan |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
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Thu, 01/03/2012 13:00 |
Tom Hosking |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
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Thu, 08/03/2012 13:00 |
Arnaud Lionnet |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| In this talk, I will present reflected backward stochastic differential equations (reflected BSDEs) and their connection with the pricing of American options. Then I will present a simple perturbative method for studying them. Under the appropriate assumptions on the coefficient, the terminal condition and the lower obstacle, similar to those used by Kobylankski, this method allows to prove the existence of a solution. I will also provide the usual comparison theorem and a new proof for a refined comparison theorem, specific to RBSDEs. | |||
