Closed form solution for maximizing CRRA type utility
Topic
This paper studies the problem of optimal investment in incomplete markets when the agents have CRRA type
utility. Closed form solutions are obtained up to some unhedgeble risk represented by a process orthogonal on
the stock price. The myopic component of the optimal portfolio is obtained by means of minimal Hellinger
martingale measure, which in our setup coincides with the minimal martingale measure. We employ Haussmann s
formula to derive the hedging component and the unhedgeble risk. We show that the optimal portfolio is robust
with respect to stopping.
The talk is based on joint work with Ulrich G. Haussmann
utility. Closed form solutions are obtained up to some unhedgeble risk represented by a process orthogonal on
the stock price. The myopic component of the optimal portfolio is obtained by means of minimal Hellinger
martingale measure, which in our setup coincides with the minimal martingale measure. We employ Haussmann s
formula to derive the hedging component and the unhedgeble risk. We show that the optimal portfolio is robust
with respect to stopping.
The talk is based on joint work with Ulrich G. Haussmann
Speakers
Additional Information
MITACS Math Finance Seminar 2006
Traian Pirvu (University of British Columbia)
