In this talk I shall first review some classical applications of filtering and stochastic control in finance. In the remainder I shall overview some of my recent research in this area including optimal trading and portfolio optimization problems in the presence of a large trader, differential information, and price impact from trading. In particular, we consider trading against a hedge fund or large trader that must liquidate a large position in a risky asset if the market price of the asset crosses a certain threshold. Liquidation occurs in a disorderly manner and negatively impacts the market price of the asset.
We consider the perspective of small investors whose trades do not induce market impact and who possess different levels of information about the liquidation trigger mechanism and the market impact.
Welcome to everyone!