This paper introduces a two-pillar cyber risk management framework to address the pervasive challenges in managing cyber risk. The first pillar, cyber risk assessment, combines insurance frequency-severity models with cybersecurity cascade models to capture the unique nature of cyber risk. The second pillar, cyber capital management, facilitates informed allocation of capital for a balanced cyber risk management strategy, including cybersecurity investments, insurance coverage, and reserves. A case study, based on historical cyber incident data and realistic assumptions, demonstrates the necessity of comprehensive cost-benefit analysis for budget-constrained companies with competing objectives in cyber risk management. In addition, sensitivity analysis highlights the dependence of the optimal strategy on factors such as the price of cybersecurity controls and their effectiveness. The framework's implementation across a diverse range of companies yields general insights on cyber risk management.