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 F to a larger filtration G if the information starts growing up to a positive time. Then we study the case G = F ∨ H when there exists a second special semi-martingale Y enjoying the predictable representation property with respect to H. We establish conditions under which the triplet (X, Y, [X, Y]) enjoys the predictable representation property with respect to G.

Calzolari, A., Torti, B. (2016). Enlargement of filtration and predictable representation property for semi-martingales. STOCHASTICS, 88(5), 1-19 [10.1080/17442508.2015.1124878].

Enlargement of filtration and predictable representation property for semi-martingales

CALZOLARI, ANTONELLA;TORTI, BARBARA
2016-01-01

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 F to a larger filtration G if the information starts growing up to a positive time. Then we study the case G = F ∨ H when there exists a second special semi-martingale Y enjoying the predictable representation property with respect to H. We establish conditions under which the triplet (X, Y, [X, Y]) enjoys the predictable representation property with respect to G.
2016
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/06 - PROBABILITA' E STATISTICA MATEMATICA
English
Con Impact Factor ISI
Semi-martingales; predictable representations property; enlargement of filtration; completeness of a financial market
Calzolari, A., Torti, B. (2016). Enlargement of filtration and predictable representation property for semi-martingales. STOCHASTICS, 88(5), 1-19 [10.1080/17442508.2015.1124878].
Calzolari, A; Torti, B
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/215608
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