The Simugram: A Robust Measure of Market Risk

James R. Thompson
Department of Statistics
Rice University



In 1738 Daniel Bernoulli created the St. Petersburg Paradox to show
that simply maximizing expectation of return was an inappropriate
strategy for pricing insurance policies. The strategy which he
recommended was to maximize the expectation of the logarithm of future
capital divided by present capital. Since Bernoulli, many investigators,
including von Neumann and Morgenstern, have attempted to  find measures
of risk which involved taking the expectation of an appropriately chosen
scalar quantity.  In this paper, I propose a robust infinite dimensional
measure of risk which can be used in practical portfolio selection.