| Potentials of a Markov process are expected suprema (2007) |
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Potentials of a Markov process are expected suprema This paper provides a new characterization of potentials of a Markov process in terms of expected suprema. This is the counterpart within potential theory of the max-plus decomposition of supermartingales, recently developped by N. El Karoui and A. Meziou, which proves to be very useful in finance (especially in the context of portfolio insurance).The representation of a potential as expected suprema of a function along the paths of the Markov process is not unique, but Follmer and Knispel give a very precise and elegant description of the maximal and minimal representing functions. |