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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.

Potentials of a Markov process are expected suprema
Hans Föllmer and Thomas Knispel
ESAIM: P&S, February 2007, Vol. 11, p. 89-101
http://dx.doi.org/10.1051/ps:2007008