Through the distinction between “real” and “virtual” links between the nodes of a graph, we develop a set of simple rules leading to scale-free networks with a tunable degree distribution exponent. Albeit sharing some similarities with preferential attachment, our procedure is both...

There exists a non-closed formula for the American put option price and non-trivial computations are required to solve it. Strong efforts have been made to propose efficient numerical techniques but few have strong mathematical reasoning to ascertain why they work well. We present an extension...