Our project concerns two major topics in mathematical finance: the assessment of risk and the evaluation of stochastic dependence in the financial and insurance markets. As tools for risk evaluation we use dynamic risk measures on processes. As risky objects we consider cash-flow streams or processes that model the evolution of financial values, and evaluate them at intermediate dates as well. We consider both the discrete multi-period and the continuous-time case, in order to provide a consistent framework for the management of risk and dynamic assessment of regulatory capital. An important objective we pursue in the project is the study of the optimal exchange of risk between economic agents who choose according to different dynamic risk measures. In particular, we want to investigate the case when one or more agents have access to a financial market and the risk can be partially hedged. In this case the analysis of the risk transfer concerns the optimal form and price of the contract as well as the optimal consumption/investment strategies. The dynamic framework means that we look at the minimum risk (or maximal utility) not just at the terminal date, but considering the whole trading period. In this way the level of satisfaction of the agents is maximized with respect to their economic situation during the whole trading period and not only at the terminal date. The optimal risk sharing problem when economic agents are endowed with a static risk measure has already been addressed by several authors in the financial literature (cf. Section 2.1), whereas, to the best of our knowledge, nothing has been done in the dynamic setting we consider here. The second contribution of this project is a detailed analysis of stochastic dependence in the financial markets, which forms the basis for portfolio risk assessment. Underestimation of risk of dependent defaults in the mortgage sector was a major reason for the current global economic crisis. This shows the importance of an appropriate modelling of dependence. In this project we aim to discuss different approaches to measure and model dependencies. That means, we study different dependence measures, like Kendall¿s tau and Spearman¿s rho, and compare them. A further main research topic is the analysis of dependent credit rating transitions. To model those, we use the approach of interacting particle systems, which provide an intuitive way to describe the observed dependence. In contrast to the previous literature we allow simultaneous rating changes, which makes a direct dependence between the firms possible. Besides the credit rating sector, we observe dependence between the credit spreads and the default-free short rate. The main task here is to model negative correlation of a positive credit spread and a positive interest rate process, which can be achieved by using Jacobi processes in a multiplicative setting.