Relative asset price bubbles

Falafala, Roseline Bilina; Jarrow, Robert A.; Protter, Philip

doi:10.1007/s10436-016-0274-8

Cited by 1 publication

(2 citation statements)

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“…Therefore it is not unreasonable to assume we can see the future of W (from which we can infer the future value of Z), but corrupted by a small amount of noise. We use the terms given in (15) and (16). More precisely, the HFT trader would want to know the information of W 1 in this example, which would then give him information regarding the future evolution of the stock price Z.…”

Section: A Current Example From Industrymentioning

confidence: 99%

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Progressive Filtration Expansions via a Process, With Applications to Insider Trading

Kchia¹,

Protter

2015

Int. J. Theor. Appl. Finan.

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In this paper we study progressive filtration expansions with càdlàg processes. Using results from the theory of the weak convergence of σ-fields, we first establish a semimartingale convergence theorem. Then we apply it in a filtration expansion with a process setting and provide sufficient conditions for a semimartingale of the base filtration to remain a semimartingale in the expanded filtration. Applications to the expansion of a Brownian filtration are given. The paper concludes with applications to models of insider trading in financial mathematics. * Let D be the space of càdlàg 1 functions from [0, T ] into R. Let Λ be the set of time changes from [0, T ] into [0, T ], i.e. the set of all continuous strictly increasing functions λ : [0, T ] → [0, T ] such that λ(0) = 0 and λ(T ) = T . We define the Skorohod distance as follows d S (x, y) = inf λ∈Λ ||λ − Id|| ∞ ∨ ||x − y • λ|| ∞for each x and y in D. Let (X n ) n≥1 and X be càdlàg processes (i.e. whose paths are in D), indexed by [0, T ] and defined on (Ω, H, P ). We will write X n P → X when (X n ) n≥1 converges in probability under the Skorohod J 1 topology to X i.e. when the sequence of 1 French acronym for right-continuous with left limits

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Section: A Current Example From Industrymentioning

confidence: 99%

“…Since the former seems unreasonable, we prefer the latter. This can be finessed by a new concept known as local NFLVR, as explained in the thesis of Roseline Bilina-Falafala [15], or in [16].…”

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confidence: 99%