When you have any kind of situation like that, the objective function almost always has discontinuous first derivatives. You have abrupt changes of behaviour between buy and sell, rather than smooth transitions between . You do not, for example, buy and sell according to a sine wave or according to Bessel functions: you effectively react according to unpredictable non-smooth external stimuli and abruptly change state.
Any optimization routine that relies upon jacobians or hessians cannot deal with those kinds of systems.
You need an optimization routine such as Genetic Algorithm (ga) which does not require that the functions be smooth.
It seems to me that if you had 100% accurate knowledge of the future, that you could achieve absolute best optimization. But you will never have 100% accurate knowledge of the future -- so it seems to me that your real problem is to try to pick the best forecasting algorithm that predicts the future the most accurately, with ability to make (possibly large) corrections based upon the "actual" data. You would have to test such algorithms multiple times over different scenarios in order to decide which algorithm was best overall (which is not necessarily going to be the one that optimizes best for any one scenario.)
