18 research outputs found
A Bound on the Financial Value of Information
Abstract --It will be shown that each bit of information at most doubles the resulting wealth in the general stock market setup. This information bound on the growth of wealth is actually' attained for certain probability distributions on the market investigated by Kelly. The bound will be shown to be a special case of the result that the increase in exponential growth of wealth achieved with true knowledge of the stock market distribution F over that achieved with incorrect knowledge G is bounded above by D( FllG), the entropy of F relative to G
Optimized Bacteria are Environmental Prediction Engines
Experimentalists have observed phenotypic variability in isogenic bacteria
populations. We explore the hypothesis that in fluctuating environments this
variability is tuned to maximize a bacterium's expected log growth rate,
potentially aided by epigenetic markers that store information about past
environments. We show that, in a complex, memoryful environment, the maximal
expected log growth rate is linear in the instantaneous predictive
information---the mutual information between a bacterium's epigenetic markers
and future environmental states. Hence, under resource constraints, optimal
epigenetic markers are causal states---the minimal sufficient statistics for
prediction. This is the minimal amount of information about the past needed to
predict the future as well as possible. We suggest new theoretical
investigations into and new experiments on bacteria phenotypic bet-hedging in
fluctuating complex environments.Comment: 7 pages, 1 figure;
http://csc.ucdavis.edu/~cmg/compmech/pubs/obepe.ht
The Value of Information for Populations in Varying Environments
The notion of information pervades informal descriptions of biological
systems, but formal treatments face the problem of defining a quantitative
measure of information rooted in a concept of fitness, which is itself an
elusive notion. Here, we present a model of population dynamics where this
problem is amenable to a mathematical analysis. In the limit where any
information about future environmental variations is common to the members of
the population, our model is equivalent to known models of financial
investment. In this case, the population can be interpreted as a portfolio of
financial assets and previous analyses have shown that a key quantity of
Shannon's communication theory, the mutual information, sets a fundamental
limit on the value of information. We show that this bound can be violated when
accounting for features that are irrelevant in finance but inherent to
biological systems, such as the stochasticity present at the individual level.
This leads us to generalize the measures of uncertainty and information usually
encountered in information theory
The History of the Quantitative Methods in Finance Conference Series. 1992-2007
This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.