Applied Mathematics Colloquia by Nicole Bauerle: Optimal Investment in Ambiguous Financial Markets with Learning

 

Optimal Investment in Ambiguous Financial Markets with Learning

 

 

We consider the classical multi-asset Merton investment problem under drift uncertainty, i.e. the asset price dynamics are given by geometric Brownian motions with constant but unknown drift coefficients. The investor assumes a prior drift distribution and is able to learn by observing the asset prize realizations during the investment horizon. While the solution of an expected utility maximizing investor with constant relative risk aversion (CRRA) is well known, we consider the optimization problem under risk and ambiguity preferences by means of the KMM (Klibanoff, Marinacci and Mukerji, 2005) approach. Here, the investor maximizes a double certainty equivalent. The inner certainty equivalent is for given drift coefficient, the outer is based on a drift distribution. Assuming also a CRRA type ambiguity function, it turns out that the optimal strategy can be stated in terms of the solution without ambiguity preferences but an adjusted drift distribution. We rely on some duality theorems to prove our statements. Based on our theoretical results, we are able to shed light on the impact of the prior drift distribution as well as the consequences of ambiguity preferences via the transfer to an adjusted drift distribution. We illustrate our findings with a numerical study.  If time allows we will briefly discuss how these ideas can be used for other stochastic dynamic optimization problems.

 

The talk is based on a joint work with Antje Mahayni.