13:00
1pm Kawei Wang
\newline Title: A Model of Behavioral Consumption in Contnuous Time
\newline 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.
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1.20 Rasmus Wissmann
\newline Title: A Principal Component Analysis-based Approach for High-Dimensional PDEs in Derivative Pricing
\newline 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
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1.40 Pedro Vitoria
\newline Title: Infinitesimal Mean-Variance and Forward Utility
\newline 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.