|Date: Tuesday, November 18, 2008
Title: Ziwet Lectures: Some Stochastic Control Problems in Mathematical Finance
Abstract: We formulate and review a class of stochastic control problems, collectively known under the rubric of Ã¢â‚¬Å“portfolio optimizationÃ¢â‚¬Â, that arise in the mathematics of finance. Ideas from convex duality play a prominent role in the resolution of these problems; so does the theory of parabolic partial differential equations, under certain strong conditions on the financial market structure. Under less stringent conditions, stochastic analogues of the classical Hamilton-Jacobi-Bellman equation emerge as particularly relevant in this context, in connection with ideas and results from Ã¢â‚¬ËœbackwardsÃ¢â‚¬â„¢ stochastic equations and the Ito-Wentzell formula for random fields. Using such tools, feedback formulae become available for the investorÃ¢â‚¬â„¢s optimal strategies, based on his current level of wealth. Recent progress on these issues will be surveyed, and some open questions will be mentioned.
Speaker: Ioannis Karatzas
Institution: University of Columbia