Section: New Results

Merton problem

Participant : J.P. Quadrat.

We consider a Merton problem corresponding to the optimization of two assets where the risky one follows the Dow Jones index and the second one has a sure reward. An empirical method has been found last year inducing very important return during a period from 1900 until 1980. It is close to the current practice of comparing the index with a filtered one. The result is much better than the standard stochastic control method which is based on an identified return process very often stationary. In fact the return process is not stationary and it is very difficult to identify the drift term locally but it is more easy to test if the drift is locally greater or smaller than the return of the sure asset. The corresponding theory is well studied for example in the Basseville Nikiforov [2] book. We are exploring this point of view to justify the empirical method found. A paper on the subject is under development.