A Note on the Strong Predictable Representation Property and Enlargement of Filtration

Antonella Calzolari and Barbara Torti
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Antonella Calzolari: Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, I 00133 Roma, Italy
Barbara Torti: Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, I 00133 Roma, Italy

Mathematics, 2022, vol. 10, issue 10, 1-12

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.

Keywords: predictable representations property; enlargement of filtration; completeness of a financial market (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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