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We call peacock an integrable process which is increasing in the convex order; such a notion plays an important role in Mathematical Finance. A deep theorem due to Kellerer states that a process is a peacock if and only if it has the same one-dimensional marginals as a martingale. Such a martingale is then said to be associated to this peacock. In this monograph, we exhibit numerous examples of peacocks and associated martingales with the help of different methods: construction of sheets, time reversal, time inversion, self-decomposability, SDE, Skorokhod embeddings… They are developed in eight chapters, with about a hundred of exercises.

Business mathematics. --- Distribution (Probability theory). --- Negative binomial distribution. --- Martingales (Mathematics) --- Finance --- Distribution (Probability theory) --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Mathematical models --- Peafowl. --- Blue peafowl, Indian --- Common peafowl --- Indian blue peafowl --- Indian peafowl --- Pavo cristatus --- Peacocks --- Mathematics. --- Economics, Mathematical. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Quantitative Finance. --- Stochastic processes --- Pavo --- Distribution (Probability theory. --- Finance. --- Funding --- Funds --- Economics --- Currency question --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Economics, Mathematical . --- Mathematical economics --- Econometrics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Methodology