No-arbitrage under additional information for thin semimartingale models

Aksamit, Anna; Choulli, Tahir; Deng, Jun; Jeanblanc, Monique

doi:10.1016/j.spa.2018.09.005

Cited by 12 publications

(33 citation statements)

References 29 publications

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“…Suppose the finite predictable constraint condition with the constraint processes α k , 1 ≤ k ≤ n. Let e k (1 ≤ k ≤ n) be a bounded continuous real function such that e k (α k ) = 0 on the time support set D of µ, and |e k (x)| ≤ c(|x| ∧ 1), x ∈ E, for some constant c. Theorem 3.3. Suppose that µ satisfies the finite F predictable constraint condition with constraint processes α k , 1 ≤ k ≤ n, satisfying identity (2). Suppose D ⊂ {β = 0}.…”

Section: The Main Resultsmentioning

confidence: 99%

“…In recent times, the class of the information changes which preserve the market viability has become a subject in itself. See, for example, the papers [1,2,8,20]. According to these papers, a major feature of that class is that the information changes satisfy some specific structural conditions.…”

Section: The Problem and The Contextmentioning

confidence: 99%

“…The present paper takes part in the same program of [20]. Following the classic settings of the initial or progressive enlargement of filtration, the papers [1,2,8] provide conditions to have the full viability. The paper [20] succeeds to do the work beyond the classic settings, with a new necessary and sufficient condition for the full viability under the martingale representation property.…”

Section: The Problem and The Contextmentioning

confidence: 99%

“…Consider always an integer valued random measure µ with its compensator ν, satisfying the finite predictable constraint condition with constraint processes α k , 1 ≤ k ≤ n, satisfying identity (2). Suppose that D = {β = 0} = ∪ 1≤n<N [S n ], where S n are mutually avoiding F totally inaccessible stopping times and N a finite or infinite integer.…”

Section: Case Of Totally Inaccessible Supportmentioning

confidence: 99%

“…and β = ∆M satisfy identity (2). Suppose that, for any S n , the vectors γ i,Sn , 1 ≤ i ≤ d, span the whole space R n (so that n ≤ d).…”

Section: Case Of Totally Inaccessible Supportmentioning

confidence: 99%

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Martingale representation processes and applications in the market viability under information flow expansion

Song

2017

ESAIM: ProcS

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Abstract. When the martingale representation property holds, we call any local martingale which realizes the representation a representation process. There are two properties of the representation process which can greatly facilitate the computations under the martingale representation property. On the one hand, the representation process is not unique and there always exists a representation process which is locally bounded and has pathwise orthogonal components outside of a predictable thin set. On the other hand, the jump measure of a representation process satisfies the finite predictable constraint, which implies the martingale projection property. In this paper, we give a detailed account of these properties. As application, we will prove that, under the martingale representation property, the full viability of an expansion of market information flow implies the drift multiplier assumption.

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Section: The Main Resultsmentioning

confidence: 99%

Section: The Problem and The Contextmentioning

confidence: 99%

Section: The Problem and The Contextmentioning

confidence: 99%

Section: Case Of Totally Inaccessible Supportmentioning

confidence: 99%

“…and β = ∆M satisfy identity (2). Suppose that, for any S n , the vectors γ i,Sn , 1 ≤ i ≤ d, span the whole space R n (so that n ≤ d).…”

Section: Case Of Totally Inaccessible Supportmentioning

confidence: 99%

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Martingale representation processes and applications in the market viability under information flow expansion

Song

2017

ESAIM: ProcS

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No-arbitrage under a class of honest times

et al. 2017

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This paper quantifies the interplay between the non-arbitrage notion of No-Unbounded-Profit-with-Bounded-Risk (NUPBR hereafter) and additional information generated by a random time. This study complements the one of Aksamit/Choulli/Deng/Jeanblanc [1] in which the authors studied similar topics for the case of stopping at the random time instead, while herein we are concerned with the part after the occurrence of the random time. Given that all the literature -up to our knowledge-proves that the NUPBR notion is always violated after honest times that avoid stopping times in a continuous filtration, herein we propose a new class of honest times for which the NUPBR notion can be preserved for some models. For this family of honest times, we elaborate two principal results. The first main result characterizes the pairs of initial market and honest time for which the resulting model preserves the NUPBR property, while the second main result characterizes the honest times that preserve the NUPBR property for any quasi-left continuous model. Furthermore, we construct explicitly "the-after-τ " local martingale deflators for a large class of initial models (i.e. models in the small filtration) that are already risk-neutralized.

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Log-optimal and numéraire portfolios for market models stopped at a random time

Choulli

Yansori

2022

Finance Stoch

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No-arbitrage under additional information for thin semimartingale models

Cited by 12 publications

References 29 publications

Martingale representation processes and applications in the market viability under information flow expansion

Martingale representation processes and applications in the market viability under information flow expansion

No-arbitrage under a class of honest times

Log-optimal and numéraire portfolios for market models stopped at a random time

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