  We solve robust optimization problem and show the example of the market model
for which the worst case measure is not a martingale measure. In our model the
instantaneous interest rate is determined by the Hull-White model and the
investor employs the HARA utility to measure his satisfaction.To protect
against the model uncertainty he uses the worst case measure approach. The
problem is formulated as a stochastic game between the investor and the market
from the other side. PDE methods are used to find the saddle point and the
precise verification argument is provided.
