Topic
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, exact sampling of the first passage event can be done for a Levy process with unbounded variation, if the process can be embedded in a subordinated standard Brownian motion.
Abstract: We show that exact sampling of the first passage event can be done for a Levy process with unbounded variation, if the process can be embedded in a subordinated standard Brownian motion. By sampling a series of first exit events of the Brownian motion and first passage events of the subordinator, the first passage event of interest can be obtained. The sampling of the first exit time and pre-exit location of the Brownian motion may be of independent interest.
4 citations
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TL;DR: In this article, the spectral heat content for time-changed killed Brownian motions on C1,1 open sets was investigated for either a subordinator or an inverse subordinator, with the underlying Laplace exponent being regularly varying at \infty with index \beta \in (0, 1).
Abstract: The spectral heat content is investigated for time-changed killed Brownian motions on C1,1 open sets, where the time change is given by either a subordinator or an inverse subordinator, with the underlying Laplace exponent being regularly varying at \infty with index \beta \in (0, 1). In the case of inverse subordinators, the asymptotic limit of the spectral heat content is shown to involve a probabilistic term depending only on \beta \in (0, 1). In contrast, in the case of subordinators, this universality holds only when \beta \in ( 1/2 , 1).
4 citations
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TL;DR: In this paper, reaction-diffusion equations are used to model systems that combine reactions with diffusive motion, and they are one of the most common mathematical models in the natural sciences.
Abstract: Reaction-diffusion equations are one of the most common mathematical models in the natural sciences and are used to model systems that combine reactions with diffusive motion. However, rather than ...
4 citations
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TL;DR: In this article, the authors proposed a method to correct for simulation bias in the Monte Carlo valuation of options with payoffs depending on the extreme value(s) of the underlying which is driven by a special Levy process, namely a normal inverse Gaussian (NIG) or a variance gamma (VG) process.
Abstract: Ribeiro and Webber (2006) propose a method to correct for simulation bias in the Monte Carlo valuation of options with pay-offs depending on the extreme value(s) of the underlying which is driven by a special Levy process, namely a normal inverse Gaussian (NIG) or a variance gamma (VG) process. The proposed method was already successfully used by Beaglehole et al. (1997) and El Babsiri and Noel (1998) when the underlying follows a Brownian motion. Unfortunately, Ribeiro and Webber, in their attempt to exploit well-known subordinator representations of NIG and VG processes, overlook the fact that these subordinator representations lead to discontinuous subordinators. Therefore their correction method ‘overcorrects’ the simulation bias by magnitudes, resulting in a much bigger simulation bias with reversed sign. We point out where the assumption of a continuous subordinator is implicitly used in the paper of Ribeiro and Webber (2006). Furthermore, by applying the unbiased Monte Carlo valuation appr...
4 citations