The strong predictable representation property of semi-martingales and the notion of enlargement of filtration meet naturally in modeling financial markets, and theoretical problems arise. Here, first, we illustrate some of them through classical examples. Then, we review recent results obtained by studying predictable martingale representations for filtrations enlarged by means of a full process, possibly with accessible components in its jump times. The emphasis is on the non-uniqueness of the martingale enjoying the strong predictable representation property with respect to the same enlarged filtration.

Calzolari, A., Torti, B. (2022). A note on the strong predictable representation property and enlargement of filtration. MATHEMATICS, 10(10) [10.3390/math10101783].

A note on the strong predictable representation property and enlargement of filtration

Calzolari, Antonella;Torti, Barbara
2022-05-01

Abstract

The strong predictable representation property of semi-martingales and the notion of enlargement of filtration meet naturally in modeling financial markets, and theoretical problems arise. Here, first, we illustrate some of them through classical examples. Then, we review recent results obtained by studying predictable martingale representations for filtrations enlarged by means of a full process, possibly with accessible components in its jump times. The emphasis is on the non-uniqueness of the martingale enjoying the strong predictable representation property with respect to the same enlarged filtration.
mag-2022
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/06 - PROBABILITA' E STATISTICA MATEMATICA
English
predictable representations property
enlargement of filtration
completeness of a financial market
Calzolari, A., Torti, B. (2022). A note on the strong predictable representation property and enlargement of filtration. MATHEMATICS, 10(10) [10.3390/math10101783].
Calzolari, A; Torti, B
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/302949
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