Admissible investment strategies in continuous trading

We consider a situation where relative prices of assets may change continuously and also have discrete jumps at random time points. The problem is the one of portfolio optimization. If the utility function used is the logarithm, we first argue that an optimal investment plan exists. Secondly, we show that any such plan has a certain optimality property known to hold also in discrete time models. Moreover, we show that this optimality criterion can be simplified significantly. In particular we show how admissibility can be related directly to observable characteristics of the investment strategy.