Prof. Karatzas (Columbia) will give a public lecture on on Dec 17 (Monday) at the Institute for Advanced Studies, Vienna from 4 - 5:30 p.m. HS. 2 "Probabilistic Aspects of Portfolio Analysis" Abstract We formulate and discuss notions such as growth rate, diversity, and arbitrage, that arise naturally in the study and analysis of portfolios. Relations among these notions are discussed, including examples of diverse markets that lead to arbitrage opportunities; some optimization problems are posed and solved; and a couple of open questions are suggested. (Joint work with Robert Fernholz.)