On the weak representation property in progressively enlarged filtrations with an application in exponential utility maximization

Tella, Paolo Di

doi:10.1016/j.spa.2019.03.013

Cited by 7 publications

(6 citation statements)

References 14 publications

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“…In summary, also if F is progressively enlarged by a random time τ , the case studied in the present paper cannot be covered by [3] nor by [8].…”

Section: Introductionmentioning

confidence: 85%

“…In Di Tella [8], the WRP in G is obtained under the assumptions that F-martingales are G-martingales (that is, if the immersion property holds) and P[τ = σ < +∞] = 0, for all F-stopping times σ (that is, if τ avoids F stopping times). If, from one side, the independent enlargement is a special case of the immersion property, on the other side, the avoidance of stopping times yields that τ cannot be charged by the jumps of F-local martingales.…”

Section: Introductionmentioning

confidence: 99%

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On the Propagation of the Weak Representation Property in Independently Enlarged Filtrations: The General Case

Tella

2021

J Theor Probab

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In this paper, we investigate the propagation of the weak representation property (WRP) to an independently enlarged filtration. More precisely, we consider an $${\mathbb {F}}$$ F -semimartingale X possessing the WRP with respect to $${\mathbb {F}}$$ F and an $${\mathbb {H}}$$ H -semimartingale Y possessing the WRP with respect to $${\mathbb {H}}$$ H . Assuming that $${\mathbb {F}}$$ F and $${\mathbb {H}}$$ H are independent, we show that the $${\mathbb {G}}$$ G -semimartingale $$Z=(X,Y)$$ Z = ( X , Y ) has the WRP with respect to $${\mathbb {G}}$$ G , where $${\mathbb {G}}:={\mathbb {F}}\vee {\mathbb {H}}$$ G : = F ∨ H . In our setting, X and Y may have simultaneous jump-times. Furthermore, their jumps may charge the same predictable times. This generalizes all available results about the propagation of the WRP to independently enlarged filtrations.

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“…In summary, also if F is progressively enlarged by a random time τ , the case studied in the present paper cannot be covered by [3] nor by [8].…”

Section: Introductionmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

On the Propagation of the Weak Representation Property in Independently Enlarged Filtrations: The General Case

Tella

2021

J Theor Probab

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“…Then {(T n , V n )} n≥1 is a m.p.p. on (Ω, F , F, P ) and Theorem 3.1 applies to it, since (11) holds and F 0 ⊂ F .…”

Section: Propagation Of Weak Martingale Representation Under Enlargem...mentioning

confidence: 99%

“…As far as the case of initial enlargement is concerned we recall the contributions of Amendinger [1], Amendinger, Becherer and Schweizer [2], Grorud and Pontier [14] and the more recent paper of Fontana [13]. In the framework of progressive enlargement, motivated by the applications in credit risk modeling, most of the authors deal with the enlargement by the natural filtration of the occurrence process of a random time and among the others we mention the seminal paper of Kusuoka [22], the contributions of Jeanblanc and Le Cam [19], Jeanblanc and Song [19], Di Tella [11], Di Tella and Engelbert [25]. Some authors discuss the case when H is the natural filtration of a semimartingale (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Martingale representations in progressive enlargement by multivariate point processes

Calzolari¹,

Torti²

2021

Preprint

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We show that all local martingales with respect to the initially enlarged natural filtration of a vector of multivariate point processes can be weakly represented up to the minimum among the explosion times of the components. We also prove that a strong representation holds if any multivariate point process of the vector has almost surely infinite explosion time and discrete mark's space. Then we provide a condition under which the components of the multidimensional local martingale driving the strong representation are pairwise orthogonal.

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“…Thus, it is natural to ask whether the converse statement holds, i.e., if a process has a strong property of predictable representation with respect to {F t } under which conditions this will also remain true for filtration {G t }. The conditions for the stability of the strong property of predictable representation under enlargement of filtration for a semimartingale X are discussed in [12], and for the stability of the weak property of predictable representation for semimartingales, they are discussed in [13]. Let us mention that under initial enlargement or when enlargement starts from a trivial σ-algebra, this property, in general, is not preserved (see [12]).…”

Section: Introductionmentioning

confidence: 99%

Concepts of Statistical Causality and Strong and Weak Properties of Predictable Representation

Valjarević

2024

Mathematics

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The paper considers the statistical concept of causality in continuous time, which is based on Granger’s definition of causality. We give necessary and sufficient conditions, in terms of statistical causality, for the preservation of the strong property of predictable representation for stopped martingales when filtration is decreased. This concept of causality is also connected to the preservation of the strong property of predictable representation under a change in measure. In addition, we give conditions, in terms of statistical causality, for martingales to have strong and weak properties of predictable representation. The results are applied to the problem of pricing claims in incomplete financial markets.

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On the weak representation property in progressively enlarged filtrations with an application in exponential utility maximization

Cited by 7 publications

References 14 publications

On the Propagation of the Weak Representation Property in Independently Enlarged Filtrations: The General Case

On the Propagation of the Weak Representation Property in Independently Enlarged Filtrations: The General Case

Martingale representations in progressive enlargement by multivariate point processes

Concepts of Statistical Causality and Strong and Weak Properties of Predictable Representation

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