Hedging Problems with Stochastic Parameters

Speaker(s): 
Date: 
February 13, 2003 - 12:00pm
Location: 
Bldg. 90
Seminar Host/Point of Contact: 

This talk concerns the problems of quadratic hedging and mean-variance portfolio selection in an incomplete market with continuous trading, multiple assets, and Brownian information. In particular, we consider the case where the parameters describing the market model (drift and volatility) are random processes. Such a situation arises, for instance, when the drift and volatility coefficients are estimated online using real-time data. We approach these problems from the perspective of linear-quadratic (LQ) optimal control and backward stochastic differential equations (BSDEs); that is, we focus on the so-called stochastic Riccati equation (SRE) associated with the problem. Our primary theoretical contribution is a proof of existence and uniqueness of solutions of the SRE associated with the quadratic hedging and mean-variance problems. In addition, we derive closed form expressions for the optimal portfolios and efficient frontier in terms of the solution of the SRE. A generalization of the Mutual Fund Theorem is also obtained. An application of these results to the problem of optimal hedging of a partially observed liability will also be discussed. Andrew Lim obtained his PhD in Systems Engineering from the Australian National University in 1998. His interests include the areas of stochastic control, financial engineering, optimization, and applied probability, and his research has been published in journals including the IEEE Transactions on Automatic Control, SIAM Journal on Control and Optimization, Automatica, and Mathematics of Operations Research. During the 2001-2002 academic year, he was a visiting assistant professor in the Department of Industrial Engineering and Operations Research at Columbia University, and joined the Industrial Engineering and Operations Research Department at the University of California (Berkeley) in 2002. For more information about this seminar, please contact: Kristina LaCommare(510) 486-4718

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