Risk management is the process by which various financial risk exposures are identified, measured, and controlled. Financial risks can be defined as those that relate to possible losses in financial markets, such as losses due to interest rate movements or defaults on financial obligations. Generally, financial risks are classified into the broad categories of market risks, credit risks, liquidity risks, operational risks, and legal risks. This study comprises three essays on risk management. In the first essay "Stress Testing for Two-stage Transmission Stress Events", we use the two-stage conditional probability distributions to compute a new loss exposure measure for stress events that may have two-stage sequential impacts on various markets. In the second essay "Estimating Extreme Correlation for the EVT-type VaR - a Copula Approach", we propose to use the Clayton copula to derive a time-varying correlation model for calculating the extreme value theory (EVT) type Value at Risk (VaR). In the third essay "A Poisson Model with Common Shocks for CDO Valuation", we show that the implementation of CDO valuation models assuming conditional dependence can be made more efficient.