# Andrew Papanicolaou - Princeton University

**Starts:**4:00 pm on Thursday, October 4, 2012

**Ends:**5:00 pm on Thursday, October 4, 2012

**Location:**MCS Room 148

Title: Dimension reduction of the Bellman equations for maximum expected utility with partial information in discrete time.
Absract: The full availability of information in nancial markets is something that is often assumed when working with models. However, parameters such as an asset's volatility and rate of return are not known and need to be estimated from past data. In this regard, the optimization of expected utility of wealth over a set of admissible trading strategies becomes a ltering problem, wherein the investor must use the ltration generated by past events to make the optimal decision for future returns. It turns out that this non-Markovian problem can be Markovianized once the dynam- ics of the lter are determined, but this Markovianized problem requires optimization over an innite dimensional eld. However, there is a class of perturbation models for which the Markovianized prob- lem is well-approximated by an unperturbed nite dimensional problem. This approximation to the perturbed problem is analyzed, and there is found to be an information premium in the market.