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Probability and Computational Finance Seminar
Christoph Frei
University of Alberta, Canada
Title: BSDEs in utility maximization with BMO market price of risk

Abstract: Power utility maximization is closely related to backward stochastic differential equations (BSDEs). After revisiting this link, we study the questions of existence, uniqueness and boundedness of the corresponding BSDE solutions when the market price of risk is only of BMO type, generalizing models with bounded mean-variance tradeoff. In a Brownian setting, we give sufficient and necessary conditions for the existence of solutions to such equations and show that there is always a continuum of distinct square-integrable solutions. This relies on the fact that contrary to the classical Itô representation a multiplicative L2-analogue in terms of stochastic exponentials is not unique. After providing interesting examples that highlight various pathologies, we derive minimal sufficient conditions for the boundedness of BSDE solutions in a general continuous filtration. The talk is based on joint work with Markus Mocha and Nicholas Westray.

Date: Monday, April 18, 2011
Time: 5:00 pm
Location: Wean Hall 6423
Submitted by:  Dmitry Kramkov