Martingale representations in progressive enlargement by multivariate point processes
Abstract
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 mark's space. Then we provide a condition under which the components of the multidimensional local martingale driving the strong representation are pairwise orthogonal.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2021
- DOI:
- 10.48550/arXiv.2107.04087
- arXiv:
- arXiv:2107.04087
- Bibcode:
- 2021arXiv210704087C
- Keywords:
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- Mathematics - Probability