The book delves into the mathematical concepts of peacocks and martingales, emphasizing their significance in finance. It employs diverse techniques, including time inversion and Skorokhod embeddings, to analyze these phenomena, providing a comprehensive exploration of their applications and implications within mathematical finance.
Penalising a process is to modify its distribution with a limiting procedure, thus defining a new process whose properties differ somewhat from those of the original one. We are presenting a number of examples of such penalisations in the Brownian and Bessel processes framework. The Martingale theory plays a crucial role. A general principle for penalisation emerges from these examples. In particular, it is shown in the Brownian framework that a positive sigma-finite measure takes a large class of penalisations into account.