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Probability and Computational Finance Seminar
Ioannis Karatzas Columbia University Title: Stable Models of Large Equity Markets Abstract: We study models for large equity markets, whose stability properties are in broad agreement with observations on the distribution of capital in the U.S. equity markets over the period 1920-2010.These models assign, to different stocks, growth rates and variances that depend both on name and on relative capitalization rank. The models are able realistically to capture the observed stability of capital distribution, while being simple enough to allow for rather detailed analytic study. The methodologies used in this study touch upon the question of triple points for systems of interacting diffusions; in particular, some choices of parameters may permit triple (or higher-order) points to occur, but we show that this has no resultant effect on any of the stability properties.The theory we develop has connections with the analysis of Queueing Networks in heavy traffic, as well as with models of competing particle systems in Statistical Mechanics and with the Sherrington-Kirkpatrick model for spin-glasses.References:T. Ichiba and I. Karatzas, On collisions of Brownian particles, Ann. Appl. Probab. 20 (2010) 951-977.T. Ichiba, V. Papathanakos, A. Banner, I. Karatzas and E. R. Fernholz, Hybrid Atlas Models, Ann. Appl. Probab., to appear (2011). Date: Friday, September 17, 2010 Time: 4:30 pm Location: Wean Hall 8220 Submitted by: Steve Shreve |