42 citations · 89 across the 8 of their papers we have counts for
11 papers
Necessity of weak subordination for some strongly subordinated Lévy processes
Boris Buchmann, Kevin W. Lu
Consider the strong subordination of a multivariate Lévy process with a multivariate subordinator. If the subordinate is a stack of independent Lévy processes and the components of…
Calibration for Weak Variance-Alpha-Gamma Processes
Boris Buchmann, Kevin W. Lu, Dilip B. Madan
The weak variance-alpha-gamma process is a multivariate Lévy process constructed by weakly subordinating Brownian motion, possibly with correlated components with an alpha-gamma su…
Selfdecomposability of Weak Variance Generalised Gamma Convolutions
Boris Buchmann, Kevin W. Lu, Dilip B. Madan
Weak variance generalised gamma convolution processes are multivariate Brownian motions weakly subordinated by multivariate Thorin subordinators. Within this class, we extend a res…
Functional Laws for Trimmed Levy Processes
Boris Buchmann, Yuguang F. Ipsen, Ross A. Maller
Two different ways of trimming the sample path of a stochastic process in D[0, 1]: global ("trim as you go") trimming and record time ("lookback") trimming are analysed to find con…
Weak Subordination of Multivariate Lévy Processes and Variance Generalised Gamma Convolutions
Boris Buchmann, Kevin Lu, Dilip B. Madan
Subordinating a multivariate Lévy process, the subordinate, with a univariate subordinator gives rise to a pathwise construction of a new Lévy process, provided the subordinator an…
Processes of rth Largest
Boris Buchmann, Ross Maller, Sidney Resnick
For integers , we treat the th largest of a sample of size as an -valued stochastic process in which we denote . We show th…
Multivariate Subordination using Generalised Gamma Convolutions with Applications to V.G. Processes and Option Pricing
Boris Buchmann, Benjamin Kaehler, Ross Maller +1
We unify and extend a number of approaches related to constructing multivariate Variance-Gamma (V.G.) models for option pricing. An overarching model is derived by subordinating mu…
Distributional representations and dominance of a Lévy process over its maximal jump processes
Boris Buchmann, Yuguang Fan, Ross A. Maller
Distributional identities for a Lévy process , its quadratic variation process and its maximal jump processes, are derived, and used to make "small time" (as $t\downarro…
Limit experiments of GARCH
Boris Buchmann, Gernot Müller
GARCH is one of the most prominent nonlinear time series models, both widely applied and thoroughly studied. Recently, it has been shown that the COGARCH model (which was introduce…
Integrated functionals of normal and fractional processes
Boris Buchmann, Ngai Hang Chan
Consider , , , where is a normal process and is a measurable real-valued function satisfying $Ef(N_0)^…
Asymptotic theory of least squares estimators for nearly unstable processes under strong dependence
Boris Buchmann, Ngai Hang Chan
This paper considers the effect of least squares procedures for nearly unstable linear time series with strongly dependent innovations. Under a general framework and appropriate sc…