First Year Presentations
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Thu, 13/10/2011 13:00 |
various |
Mathematical Finance Internal Seminar  |
DH 1st floor SR |
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1pm Kawei Wang
Title: A Model of Behavioral Consumption in Contnuous Time Abstract: Inspired by Jin and Zhou (2008), we try to construct a model of consumption within the framework of Prospect Theory and Cumulative Prospect Theory in continuous time. 1.20 Rasmus Wissmann Title: A Principal Component Analysis-based Approach for High-Dimensional PDEs in Derivative Pricing Abstract: Complex derivatives, such as multi asset and path dependent options, often lead to high-dimensional problems. These are generally hard to tackle with numerical PDE methods, because the computational effort necessary increases exponentially with the number of dimensions. We investigate a Principal Component Analysis-based approach that aims to make the high-dimensional problem tractable by splitting it into a number of low-dimensional ones. This is done via a diagonalization of the PDE according to the eigenvectors of the covariance matrix and a subsequent Taylor-like approximation. This idea was first introduced by Reisinger and Wittum for the basic case of a vanilla option on a basket of stocks [1]. We aim to extend the approach to more complex derivatives and markets as well as to develop higher order versions. In this talk we will present the basic ideas, initial results for the example of a ratchet cap under the LIBOR Market Model and the current plans for further research. [1] C. Reisinger and G. Wittum, Efficient Hierarchical Approximation of High-Dimensional Option Pricing Problems, SIAM Journal of Scientific Computing, 2007:29 1.40 Pedro Vitoria Title: Infinitesimal Mean-Variance and Forward Utility Abstract: Mean-Variance, introduced by Markowitz in his seminal paper of 1952, is a classic criterion in Portfolio Theory that is still predominantly used today in real investment practice. In the academic literature, a number of interesting results have been produced in continuous-time version of this model. In my talk, I will establish a link between the multi-period Mean-Variance model and its continuous-time limit. A key feature of the results is that, under suitable but mild technical conditions, it captures the results of Forward Utility, thus establishing an important link between Mean-Variance and forward utility maximisation. |
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