Volume 11, February 2007Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday
|Page(s)||89 - 101|
|Published online||01 March 2007|
Potentials of a Markov process are expected suprema
Humboldt-Universität zu Berlin, Institut für Mathematik, Unter den Linden 6, 10099 Berlin, Germany; firstname.lastname@example.org; email@example.com
Accepted: September 2005
Expected suprema of a function f observed along the paths of a nice Markov process define an excessive function, and in fact a potential if f vanishes at the boundary. Conversely, we show under mild regularity conditions that any potential admits a representation in terms of expected suprema. Moreover, we identify the maximal and the minimal representing function in terms of probabilistic potential theory. Our results are motivated by the work of El Karoui and Meziou (2006) on the max-plus decomposition of supermartingales, and they provide a singular analogue to the non-linear Riesz representation in El Karoui and Föllmer (2005).
Mathematics Subject Classification: 31C05 / 60J25 / 60J45
Key words: Markov processes / potentials / optimal stopping / max-plus decomposition.
© EDP Sciences, SMAI, 2007
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