Series: Bocconi & Springer Series
Hirsch, F., Profeta, C., Roynette, B., Yor, M.
2011, XXXII, 388 p.
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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.
Content Level » Research
Keywords » Brownian motion - Convex order - Markov processes - Martingales - Peacocks
Related subjects » Probability Theory and Stochastic Processes - Quantitative Finance
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