MARTINGALE REPRESENTATIONS IN PROGRESSIVE ENLARGEMENT BY MULTIVARIATE POINT PROCESSES

Antonella Calzolari () and Barbara Torti
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Antonella Calzolari: Department of Mathematics, University of Rome “Tor Vergata†, via della Ricerca Scientifica 1, Rome 00133, Italy
Barbara Torti: Department of Mathematics, University of Rome “Tor Vergata†, via della Ricerca Scientifica 1, Rome 00133, Italy

International Journal of Theoretical and Applied Finance (IJTAF), 2022, vol. 25, issue 03, 1-21

Abstract: In this paper, we show that all local martingales with respect to the initially enlarged natural filtration of a vector of multivariate point processes can be weakly represented up to the minimum among the explosion times of the components. We also prove that a strong representation holds if any multivariate point process of the vector has almost surely infinite explosion time and discrete marks space. Then we provide a condition under which the components of the multidimensional local martingale driving the strong representation are pairwise orthogonal.

Keywords: Semi-martingales; predictable representations property; enlargement of filtration; marked point processes; random measures (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0219024922500157

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