“Pragmatic Information Rates, Generalizations of the Kelly Criterion, and Financial Market Efficiency,” available on the web at

“A Theory of Pragmatic Information and Its Application to the Quasispecies Model of Biological Evolution,” BioSystems, 66, #3, 105-119 (2002), available on the web at

“Risky Business: A Review of Risk Management by Michel Crouhy, Dan Galai, and Robert Mark,” RMA Journal, available on the web.Review of Crouhy Risk Mgmt Book

Review of Crouhy Risk Mgmt Book

“How Close is Close Enough: The Limitations of Monte Carlo in Computing VaR,” paper included in the proceedings volume of the 1999 Institute for International Research Conference, “Effectively Managing and Mitigating Model Risk.”  Available on the web at

“The Geometry of VaR,” Learning Curve, Derivatives Week, November 4, 1996.  Available on the web at

THE LETTER BOX: Ed Weinberger explains how to build one of those ‘black box’ implied volatility calculators,” reprinted in Over the Rainbow, Developments in Exotic Options and Complex Swaps, edited by Robert Jarrow.

“A Stochastic Generalization of Eigen’s Theory of Natural Selection,” The Courant Institute of Mathematical Sciences, New York University Ph.D. Dissertation, 1987.