Martingale representation on enlarged filtrations: the role of the accessible jump times
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2017
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| _version_ | 1866909398718218240 |
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| author | Calzolari, Antonella Torti, Barbara |
| author_facet | Calzolari, Antonella Torti, Barbara |
| contents | We consider a filtration $\mathbb{G}$ obtained as enlargement of a filtration $\mathbb{F}$ by a filtration $\mathbb{H}$. We assume that all $\mathbb{F}$-local martingales are represented by a martingale $M$ and all $\mathbb{H}$-local martingales are represented by a martingale $N$. $M$ and $N$ are not necessarily quasi-left continuous processes and their jump times may overlap. We first analyze the contribution of the accessible jump times of $M$ and $N$ to the Jacod's dimension of the space of the $\mathcal{H}^1(\mathbb{G})$-martingales. Then we prove a new martingale representation theorem on $\mathbb{G}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1708_05858 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Martingale representation on enlarged filtrations: the role of the accessible jump times Calzolari, Antonella Torti, Barbara Probability We consider a filtration $\mathbb{G}$ obtained as enlargement of a filtration $\mathbb{F}$ by a filtration $\mathbb{H}$. We assume that all $\mathbb{F}$-local martingales are represented by a martingale $M$ and all $\mathbb{H}$-local martingales are represented by a martingale $N$. $M$ and $N$ are not necessarily quasi-left continuous processes and their jump times may overlap. We first analyze the contribution of the accessible jump times of $M$ and $N$ to the Jacod's dimension of the space of the $\mathcal{H}^1(\mathbb{G})$-martingales. Then we prove a new martingale representation theorem on $\mathbb{G}$. |
| title | Martingale representation on enlarged filtrations: the role of the accessible jump times |
| topic | Probability |
| url | https://arxiv.org/abs/1708.05858 |