This two-hour course will be given in English upon request.
Abstract:
This course deals with models for portfolio selection. We start with the most
basic but still popular model of Markowitz. This model is then extended to
include investement restrictions for example. In a next step, we replace the
variance as a measure of risk by shortfall risk measures. The most prominent
example is Value-at-Risk. We then extend the portfolio selection problem from a
single-period world to a multi-period setup. We solve the dynamic asset-only and
the dynamic asset and liability model. In the next chapter, we ask whether there
exist economic foundations for the so far ad-hoc portfolio selection models. This
leads us to study decision making under uncertainty and we compare the most
popular model - expected utility - with facts from real life decision making of
individuals under uncertainty. We finish the lecture showing how portfolio theory
can be applied to solve operation risk problems in computer networks. Besides
mathematical rigor we are equally interested to test the various models with real
world data and to highlight some difficulties dealing with data sets.
Topics
One-period mean-variance portfolio selection
Classical model of Markowitz
Extension of the classical model
Construction of the efficient frontier from market data
Parameter estimation techniques and variance-reduction algorithms
Extracting parameters of risk aversion from market data
One-period mean-downside risk portfolio selection
Practice of Value-at-Risk (VaR)
VaR and Conditional Value-at-Risk (CVaR): Definitions and properties
Mean-CVaR portfolio optimization
Numerical examples
Critique of the mean-downside risk portfolio selection approach
