Enlargement of filtration and predictable representation property for semi-martingales
Abstract
We present two examples of loss of the predictable representation property for semi-martingales by enlargement of the reference filtration. First of all we show that the predictable representation property for a square-integrable semi-martingale X does not transfer from the reference filtration F to a larger filtration G when the information starts growing up to a positive time. Then we study the case when F coincides with the natural filtration of X and G is obtained by adding the natural filtration of a second square-integrable semi-martingale, Y. We establish conditions under which the triplet (X,Y,[X,Y]) enjoys the predictable representation property with respect to G.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2013
- DOI:
- 10.48550/arXiv.1309.5766
- arXiv:
- arXiv:1309.5766
- Bibcode:
- 2013arXiv1309.5766C
- Keywords:
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- Mathematics - Probability
- E-Print:
- to appear on Stochastics