Title: Relative performance approach to robust portfolio selection
Speaker: Andrew Lim

Abstract:
Recent interest in the general topic of ``robust portfolio selection" in
the finance, economics, and optimization communities, has been motivated
largely by the observation that the solutions of classical optimal
portfolio selection problems are sensitive to statistical errors that can
arise in the model calibration stage, and that the ``real world"
performance of such portfolios can be poor if these errors are ignored.
The commonly proposed method for addressing this problem has been ``worst
case" optimization (which has it roots in statistics as well as
electrical engineering). This has led in turn to methodologies\uffff such as
``robust mean-variance portfolio selection" and ``robust utility
maximization". The primary criticism of this approach to optimal
investment, however, is that it gives rise to extremely conservative
solutions.

In this talk, we propose and analyze an alternative measure of ``robust
performance". This alternative measure differs from the typical ``worst
case expected utility" and ``worst case mean-variance"\uffff formulations that
are commonly studied in the literature in that the ``robust performance"
of a (dynamic) portfolio is evaluated not only on the basis of its
performance when there is an adversarial opponent (``nature"), but also
by its performance relative to a fully informed `benchmark investor" who
behaves optimally given complete knowledge of the otherwise ambiguous
model. This ``relative performance" approach has several important
properties: (i) decisions arising from this approach are less pessimistic
than the portfolios obtained from the typical ``worst case expected
utility" and ``worst case mean-variance" formulations, and (ii) the
dynamic ``relative performance" problem reduces to a convex static
optimization problem under reasonable choices of the benchmark portfolio.
This static problem is interesting in its own right: it can be
interpreted as a less pessimistic alternative to the single period
``worst case mean-variance" problem.