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 semi-martingale X does not transfer from the reference filtration to a larger filtration if the information starts growing up to a positive time. Then we study the case when there exists a second special semi-martingale Y enjoying the predictable representation property with respect to . We establish conditions under which the triplet (X, Y, [X, Y]) enjoys the predictable representation property with respect to .
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