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Subordinator
About: Subordinator is a research topic. Over the lifetime, 771 publications have been published within this topic receiving 15383 citations.
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TL;DR: In this paper, the authors derived a renewal type equation for the martingale option price and proved that these option prices converge to the price of an option written on geometric Brownian motion time-changed with the inverse stable subordinator.
Abstract: We consider plain vanilla European options written on an underlying asset that follows a continuous time semi-Markov multiplicative process. We derive a formula and a renewal type equation for the martingale option price. In the case in which intertrade times follow the Mittag-Leffler distribution, under appropriate scaling, we prove that these option prices converge to the price of an option written on geometric Brownian motion time-changed with the inverse stable subordinator. For geometric Brownian motion time changed with an inverse subordinator, in the more general case when the subordinator's Laplace exponent is a special Bernstein function, we derive a time-fractional generalization of the equation of Black and Scholes.
2 citations
TL;DR: The authors identify just so as a newly emerging purpose subordinator and use it to represent a case of semantic specialization where the purpose meaning wins out over the conditional meaning, thus filling the niche of informal purpose subordinators and providing an alternative to its multifunctional and semantically ambiguous competitors.
Abstract: This article identifies just so as a newly emerging purpose subordinator. Using data from the Corpus of Contemporary American English and the Corpus of Historical American English , it traces its development and steady increase in frequency from its first attestation in the mid nineteenth century to the present day. Just so is shown to represent a case of semantic specialization where the purpose meaning wins out over the conditional meaning, thus filling the niche of an informal purpose subordinator and providing an alternative to its multifunctional and semantically ambiguous competitors so that and so . With increasing grammaticalization the just so purpose subordinator also exhibits signs of intersubjectification, being coopted for syntactically independent, interpersonal uses (e.g. just so we're clear ) and culminating in the emergence of a new discourse marker in the form of just so you know in the late twentieth and early twenty-first century. To account for the emergence of purpose just so , a constructional network approach is adopted, which considers the network links to other purpose subordinators, notably so that and so .
2 citations
TL;DR: In this article, it was shown that self-decomposability is inherited from subordinator to subordinated in the case of strictly stable cone-parameter convolution semigroups.
Abstract: Extension of two known facts concerning subordination is made. The first fact is that, in subordination of $1$-dimensional Brownian motion with drift, selfdecomposability is inherited from subordinator to subordinated. This is extended to subordination of cone-parameter convolution semigroups. The second fact is that, in subordination of strictly stable cone-parameter convolution semigroups on $\mathbf{R}^d$, selfdecomposability is inherited from subordinator to subordinated. This is extended to semi-selfdecomposability.
2 citations
TL;DR: In this paper, the authors compare two types of subdiffusion applied to random motion of magnetic bright points at the solar photosphere, one is due to the inverse-time α-stable Levy process as a subordinator, another is subordinated by the αstable process.
Abstract: In this paper we compare two types of subdiffusion applied to random motion of magnetic bright points at the solar photosphere. One is due to the inverse-time α-stable Levy process as a subordinator, another is subordinated by the α-stable process. The recommendation to identify each type of subdiffusion in the solar experiment is suggested. The difference of these scenarios lies in distinct contrast to the description with the corresponding subdiffusive fractional Fokker-Planck approach, thus providing experimentalists an test to differentiate between the two subdiffusion scenarios.
2 citations
TL;DR: In this paper, the authors considered the case of a Cauchy subordinator with the property that the tail function of the canonical measure of X α is regularly varying of index − α ∈ ( − 1, 0 ) as x ↓ 0.
2 citations