Sylvain Rubenthaler

Optimal portfolio allocation strategy and optimal filter in a 
simple model : numerical issues
 
Abstract : We are interested in a model of portfolio with one riskless
asset and one risky asset whose drift is jumping between mu_1 and
mu_2. The optimal portfolio is based of the conditional probability
of  the drift to be mu_1 knowing the prices of the assets. This
conditional probability is the solution of an SDE which could be
approximated by an Euler scheme. We propose another scheme, inspired
by classical filtering theory, which is better in some sense.
 
I must add that this is a work in progress and that the fact that our
scheme is  better is not yet established in a satisfactory way.