The Doctoral Thesis is devoted to the field of risk management in insurance to ensure the solvency and financial stability of each insurance company in the European Union in line with the Solvency II framework. The present Doctoral Thesis covers the 2nd Pillar of the Solvency II regime, mainly risk management part. The enhancement of the risk assessment should be performed through a more sophisticated and sensitive risk analysis in order to ensure the stability and solvency of insurance company’s development and activity. During the research, the author has investigated the nature of risk, significance of the risk culture in insurance and importance of the System of Governance under the Solvency II framework. However, the author has also applied the Analytic Hierarchy Process and Analytic Network Process to insurance in order to improve the risk assessment and decision making within an insurance company. In addition, the author has conducted the research in order to assess the capital to cover possible losses due to the occurrence of the operational risk events using the copula theory and approved the possibility of its usage for risk assessment.