A new method has been developed to simulate the behavior of a type of mathematical process called Lévy processes, which are used in insurance and finance. This method combines different techniques from previous studies and relies on a mathematical concept called the Wiener–Hopf decomposition. By using this method, researchers were able to simulate various types of Lévy processes, including a new family called hypergeometric Lévy processes. They also showed that this method can be extended to simulate other related processes and solve complex mathematical problems.