In the first part, we provide a martingale decomposition theorem for arbitrary local martingales. Moreover, we compare this decomposition, named Radon-Nikodym decomposition, to the well known Kunita-Watanabe decomposition. Furthermore, we give examples in which the Kunita-Watanabe decomposition does not exist. Finally, we provide the Radon-Nikodym decomposition in these particular examples. The second part is dedicated to structure conditions for locally square-integrable semimartingales. In several 'structure theorems', we highlight the connection between the structure of locally square-integrable semimartingales, encoded in different 'structure conditions', and different martingale decomposition theorems of strictly positive sigma-martingale densities with respect to the local martingale part of the semimartingale under consideration. We compare these new structure conditions to the well known structure condition (SC) and the weak structure condition (SC'). Through numerous examples we highlight how these new structure conditions can be used in order to find strictly positive sigma-martingale densities. In the last part, we provide a modular model approach to large traders. The idea is to 'decompose' the different phenomena, related to the presence of a large trader in a financial market, into several modules. Here, we consider the 'price module' and the 'no arbitrage for the small trader' module. In the first one, we provide a flexible model that allows us to model the impact of the large trader on the price process. In the second module, we provide minimal assumptions that ensure that the turbulences, caused by the large trader's actions, do not lead to arbitrage opportunities for the small trader. With the help of the structure condition (SC), we provide sufficient conditions that ensure that these results hold for a large class of large trader strategies. Finally, we consider the large trader utility maximization problem. We discover new phenomena that reveal that the presence of a large trader might destabilize the financial market. These phenomena appear even though the large trader strategy is not an arbitrage strategy in the sense of the classical no arbitrage condition.