You are invited to an IEOR Monday Seminar:
 
THE DIMENSIONS OF LONG TERM GROWTH
David G. Luenberger
Department of management Science and Engineering, Stanford University
Abstract
This talk will review the fact that under some standard assumptions,
the long term growth of a portfolio is optimized by selecting the
weights of the various assets so as to maximize the expected
logarithm of the one-period return. The return is defined by a random
multiple of initial portfolio value, determined by the underlying
individual random returns. In operation, the portfolio should be
rebalanced with these weights each period. This theory is one of the
best for designing optimal portfolios. However, some investment
situations do not satisfy the assumptions required. In particular,
the assumptions are not satisfied in any situation where the state of
a portfolio cannot be fully described by its value. This includes
cases where there are transaction costs, limited liquidity, and where
external variables are critical. If other variables such as these are
needed, the log-optimal criterion does not imply optimal growth.
When there are other dimensions, aside from total value, the
transition from one period to another must be described by a random
matrix or a more general random mapping. It is impossible to take the
logarithm of these higher-dimensional transformations, and that is
why the standard theory breaks down. Nevertheless it is still
possible to formulate the optimal growth problem and characterize its
composition. In the case of random matrix transitions, the key result
is based on a theorem due to Richard Bellman, which has been
generalized by others. It is also possible to extend this result to
nonlinear mappings, which arise for instance when there are
transactions costs.
The talk will emphasize the intuitive nature of the results and the
relation between familiar mathematical results. Several examples will
be presented.
Biographical Sketch:
Prof. Luenberger received the BS degree from Caltech and the MS and
PhD degrees from Stanford University, all in electrical engineering.
His research theme "better living through mathematics" has led him to
carry out research in modern control theory, optimization, economics,
finance, and information science, and to apply these concepts in many
diverse application areas. He is author of over 80 technical papers
and six textbooks (two of which are currently used in IEOR262B and
IEOR221). He was one of the founders of the Department of
Engineering-Economic Systems at Stanford. In 1971, he served as
Technical Assistant to the President's Science Advisor in Washington
D.C. He is a fellow of the IEEE, was president of the Society of
Economic Dynamics and Control, was awarded the Oldenberger Medal by
the ASME and received the INFORMS award for expository writing. His
current research is in investment science.
 
3108 Etcheverry
Monday, 13 November 2006
3:30PM-4:30PM
 
COME EARLY! REFRESHMENTS WILL BE SERVED AT 3:00PM.