Applied Mathematics Colloquium

**Please note--Different time for this week only**

The full availability of information is often assumed in modeling nancial markets for
asset and derivative pricing, portfolio management and other applications. 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 the expected utility of the wealth of a portfolio over a set of admissible
investment strategies includes also a ltering problem, wherein the investor must use the ltration
generated by past events to make the optimal decision for future returns. This leads to a non-
Markovian stochastic optimization problem that can be Markovianized once the dynamics of the lter
are determined, but this Markovianized problem requires optimization over an in nite dimensional
set of variables. This paper analyzes a class of risky asset models for which the Markovianized
optimization problem is well-approximated by an unperturbed nite dimensional one. The dimension
reduction is considered in detail and the information premium relative to full information is assessed.