15:00 – Mete Soner (ETH Zurich)
Title: Asymptotics for the Davis-Norman problem.
Abstract: We consider the classical utility maximization in a market with transaction costs as formulated by Davis and Norman in 1991.
A precise qualitative description of the investment strategy is also obtained in this seminal paper. As the transaction costs tend to zero, it is clear that the value function converge to the limiting frictionless Merton value function. Then, the asymptotic question of importance is the rate of convergence of the value function and the so-called no-transaction region.
In this talk, we outline a very general approach that provides the solution. The main methodology is formal matched asymptotics and homogenization.
16:00 – Dirk Becherer (Humbolt U.-Berlin)
Title: Portfolio optimization under model uncertainty with incomplete preferences.
Abstract: Solutions to optimal control problems for optimal investment portfolios are notoriously sensitive to assumptions about underlying model. And it is well known that key parameters of any financial model, like the means of asset returns, can be highly uncertain.
We study a portfolio optimization problem of Merton type for an growth optimizing investor. The investor is faced with asset returns that depend on an unobservable factor process involving uncertain parameters, leading to a family of filtering problems. Under incomplete preferences of Bewley type, we show how the optimal investment strategy for such an inert investor can be constructed as an impulse control.