A note on the worst case approach for a market with a stochastic interest rate

We solve a robust optimization problem and show an example of a 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. PDE methods are used to find a saddle point and a precise verification argument is provided.