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Martingale Representations In Progressive Enlargement By Multivariate Point Processes

Author

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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)

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.

Suggested Citation

  • Antonella Calzolari & Barbara Torti, 2022. "Martingale Representations In Progressive Enlargement By Multivariate Point Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 25(03), pages 1-21, May.
    • Handle: RePEc:wsi:ijtafx:v:25:y:2022:i:03:n:s0219024922500157
    DOI: 10.1142/S0219024922500157
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