Abstract: Reinsurance is an important risk management tool for an insurer. An appropriate use of reinsurance can reduce insurance risks and the volatility of financial results, stabi- lize solvency, better withstand catastrophic events, and increase underwriting capacity. The use of reinsurance, on the other hand, incurs additional cost on the insurer in the form of reinsurance premium. This implies a classical tradeoff between risk spreading and risk retaining for the insurer in deciding reinsurance purchase. An optimal rein- surance design aims at striking a balance between these two conflicting objectives. In this talk, I will introduce some of my recent works on this topic, with a focus on risk measure minimization models and those popular risk measures including Value-at-Risk, Conditional Value-at-Risk, and Expectile, among others.