Inhalt des Dokuments
Preprint 11-2004
Optimal investments for robust utility functionals in complete market models
Author(s) :
Alexander Schied
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 11-2004
MSC 2000
- 91B28 Finance, portfolios, investment
Abstract :
We introduce a systematic approach to the problem of
maximizing the robust utility of the terminal wealth of an admissible strategy in a
general complete market model, where the robust utility functional is defined by a set $\cQ$ of
probability measures. Our main result shows that this problem can be reduced to determining a
"least favorable" measure
$Q_0\in\cQ$, which is universal in the sense that it does not depend
on the particular utility function. The robust problem is thus equivalent to a
standard utility maximization problem with respect to the "subjective" probability measure
$Q_0$. By using the Huber-Strassen theorem from
robust statistics, it is shown that $Q_0$ always exists if $\cQ$ is the core of a
2-alternating upper probability. We also discuss the problem of robust utility maximization
with uncertain drift in a Black-Scholes market and the case of "weak information" as studied
by Baudoin (2002).
Keywords :
robust utility maximization, financial markets, Radon-Nikodym derivative of capacities