Mathematical Finance Internal Seminar
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Thu, 14/10/2010 13:00 |
Mathematical Finance Internal Seminar  |
DH 1st floor SR | |
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Thu, 21/10/2010 12:45 |
Mathematical Finance Internal Seminar |
DH 1st floor SR | |
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Thu, 28/10/2010 13:00 |
Sergey Nadtochiy |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| We solve the problem of static hedging of (upper) barrier options (we concentrate on up-and-out put, but show how the other cases follow from this one) in models where the underlying is given by a time-homogeneous diffusion process with, possibly, independent stochastic time-change. The main result of the paper includes analytic expression for the payoff of a (single) European-type contingent claim (which pays a certain function of the underlying value at maturity, without any pathdependence), such that it has the same price as the barrier option up until hitting the barrier. We then consider some examples, including the Black-Scholes, CEV and zero-correlation SABR models, and investigate an approximation of the exact static hedge with two vanilla (call and put) options. | |||
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Thu, 04/11/2010 13:00 |
Nathaniel Korda |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| An agent is presented with an N Bandit (Fruit) machines. It is assumed that each machine produces successes or failures according to some fixed, but unknown Bernoulli distribution. If the agent plays for ever, how can he/she choose a strategy that ensures the average successes observed tend to the parameter of the "best" arm? Alternatively suppose that the agent recieves a reward of a^n at the nth button press for a success, and 0 for a failure; now how can the agent choose a strategy to optimise his/her total expected rewards over all time? These are two examples of classic Bandit Problems. We analyse the behaviour of two strategies, the Narendra Algorithm and the Gittins Index Strategy. The Narendra Algorithm is a "learning" strategy, in that it answers the first question in the above paragraph, and we demonstrate this remains true when the sequences of success and failures observed on the machines are no longer i.i.d., but merely satisfy an ergodic condition. The Gittins Index Strategy optimises the reward stream given above. We demonstrate that this strategy does not "learn" and give some new explicit bounds on the Gittins Indices themselves. | |||
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Thu, 11/11/2010 13:00 |
Stephen Roberts |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| This talk highlights the role of Gaussian Process models in sequential data analysis. Issues of active data selection, global optimisation, sensor selection and prediction in the presence of changepoints are discussed. | |||
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Thu, 18/11/2010 13:00 |
Jan Witte |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
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Thu, 25/11/2010 13:00 |
Mike Giles |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
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Thu, 02/12/2010 13:00 |
Gechun Liang |
Mathematical Finance Internal Seminar |
L3 |
| In [Liang, Lyons and Qian(2009): Backward Stochastic Dynamics on a Filtered Probability Space, to appear in the Annals of Probability], the authors demonstrated that BSDEs can be reformulated as functional differential equations, and as an application, they solved BSDEs on general filtered probability spaces. In this paper the authors continue the study of functional differential equations and demonstrate how such approach can be used to solve FBSDEs. By this approach the equations can be solved in one direction altogether rather than in a forward and backward way. The solutions of FBSDEs are then employed to construct the weak solutions to a class of BSDE systems (not necessarily scalar) with quadratic growth, by a nonlinear version of Girsanov's transformation. As the solving procedure is constructive, the authors not only obtain the existence and uniqueness theorem, but also really work out the solutions to such class of BSDE systems with quadratic growth. Finally an optimal portfolio problem in incomplete markets is solved based on the functional differential equation approach and the nonlinear Girsanov's transformation. The talk is based on the joint work with Lyons and Qian: http://arxiv4.library.cornell.edu/abs/1011.4499 | |||
