Since banks and insurance companies are financial institutions dealing with risks in various aspects of their business, it is important to make a general approach to the issue of risk and risk management from the perspective of these institutions. In that regard, we made a short overview of the risks these institutions are faced to as well as the methods they use for risk assessments. In order to limit our research to specific financial markets, we provided the basic characteristics of bank and insurance markets of Southeastern Europe (SEE), presenting the core indicators of development level of these markets and their legal and institutional environment related to new regulation proposed in Europe. We analyzed the level of implementation of Basel and Solvency risk assessment standards in these countries and tried to anticipate direction (s) where these markets are going to move in the coming period.