Enlargement of Filtration and a Broader Class of Utility Functions

In Financial Mathematics, the theory of enlargement of filtrations has been applied to modelling insider trading on stock markets as well as to the informational asymmetry on electricity markets. Still, when it comes to calculating the utility of market agents in either of these additional information approaches authors have exclusively considered the combination of a log-normal underlying and a log-utility. With this cancelling combination one can straight forwardly calculate expectations under the larger filtration without having to deal with potentially unknown distributional properties. In this paper, we will present a new methodology which allows to chose, in an enlargement of filtration framework, from a larger class of both utility functions and price models. We apply the method to both fields of Financial Mathematics mentioned before: First, we extend the famous Karatzas-Pikovsky insider trading scenario. Second, we utilise a well-known electricity spot model and the indifference price of electricity forwards in the presence of additional future information known to market traders