An Example of Martingale Representation in Progressive Enlargement by an Accessible Random Time

Calzolari, Antonella; Torti, Barbara

doi:10.1007/978-3-030-22285-7_4

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Kusuoka-like Representation Theorem For a General Random Time1

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2019

2024

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Cited by 4 publications

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“…Example 4.9. ( [10]) On the probability space (Ω, F, P ) consider the process M = (M t ) t∈[0,T ] defined as follows…”

Section: Kusuoka-like Representation Theorem For a General Random Timementioning

confidence: 99%

Martingale representations in dynamic enlargement setting: the role of the accessible jump times

Calzolari¹,

Torti²

2017

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Let M and N be a real F-martingale and H-martingale respectively on the same probability space, both enjoying the predictable representation property. We discuss how, under the assumption of the existence of an equivalent decoupling measure for F and H, the nature of the jump times of M and N affects the representation of the F ∨ H-martingales. More precisely we show that the multiplicity of F∨H depends on the behavior of the common accessible jump times of the two martingales. Then we propose an extension of Kusuoka's representation theorem to the case when the Brownian Motion is replaced by a semi-martingale which may jump at the default time with positive probability.

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