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Probability and Computational Finance Seminar
Scott Robertson Carnegie Mellon University Title: Portfolio Turnpikes in Incomplete Markets Abstract: Portfolio turnpikes state that, as the investment horizon increases, optimal portfolios for generic utilities converge to those of isoelastic, or power, utilities. In this talk, we will prove three types of turnpike theorems. The "abstract" turnpike, valid in a semi-martingale setting under minimal hypotheses, implies that final payoffs and portfolios converge under their myopic probabilities. The "classic" turnpike, under which convergence takes place with respect to the physical measure, follows from the abstract turnpike under an additional hypothesis of contiguity between the physical and myopic probabilities.As an example, we will consider a class of diffusion models with several assets and a single state variable. Under suitable hypotheses, in addition to the classic turnpike, an "explicit" turnpike holds, in which the limiting optimal portfolios are identified via the solution of an ergodic HJB equation. Date: Monday, February 13, 2012 Time: 5:00 pm Location: Wean Hall 5409 Submitted by: Scott Robertson |