Subordinator

About: Subordinator is a research topic. Over the lifetime, 771 publications have been published within this topic receiving 15383 citations.

Reparameterizing Marshall–Olkin copulas with applications to sampling

Abstract: It is shown that exchangeable Marshall–Olkin survival copulas coincide with a parametric family of copulas studied in [J.-F. Mai and M. Scherer, Levy-Frailty copulas, J. Multivariate Anal. 100 (2009), pp. 1567–1585]. This observation implies an alternative probabilistic interpretation in many cases and allows the transfer of known results from one family to the other. For instance, using the classical construction of [A.W. Marshall and I. Olkin, A multivariate exponential distribution, J. Am. Stat. Assoc. 62 (1967), pp. 30–44], sampling an n-dimensional Marshall–Olkin copula requires 2 n −1 exponentially distributed random variables, which is inefficient in large dimensions. Applying the alternative construction, sampling an exchangeable n-dimensional copula boils down to generating n independent exponentially distributed random variables and one path of a certain Levy subordinator, which is highly efficient in many cases. Furthermore, the alternative model and sampling methodology is generalized to high-...

CGMY and Meixner Subordinators are Absolutely Continuous with respect to One Sided Stable Subordinators.

Abstract: We describe the CGMY and Meixner processes as time changed Brownian motions. The CGMY uses a time change absolutely continuous with respect to the one-sided stable $(Y/2)$ subordinator while the Meixner time change is absolutely continuous with respect to the one sided stable $(1/2)$ subordinator$.$ The required time changes may be generated by simulating the requisite one-sided stable subordinator and throwing away some of the jumps as described in Rosinski (2001).

Fractional Skellam processes with applications to finance

Abstract: The recent literature on high frequency financial data includes models that use the difference of two Poisson processes, and incorporate a Skellam distribution for forward prices. The exponential distribution of inter-arrival times in these models is not always supported by data. Fractional generalization of Poisson process, or fractional Poisson process, overcomes this limitation and has Mittag-Leffler distribution of inter-arrival times. This paper defines fractional Skellam processes via the time changes in Poisson and Skellam processes by an inverse of a standard stable subordinator. An application to high frequency financial data set is provided to illustrate the advantages of models based on fractional Skellam processes.

Universality of the REM for Dynamics of Mean-Field Spin Glasses

Abstract: We consider a version of Glauber dynamics for a p-spin Sherrington– Kirkpatrick model of a spin glass that can be seen as a time change of simple random walk on the N-dimensional hypercube. We show that, for all p ≥ 3 and all inverse temperatures β > 0, there exists a constant γ β ,p > 0, such that for all exponential time scales, exp(γ N), with γ < γ β ,p , the properly rescaled clock process (time-change process) converges to an α-stable subordinator where α = γ/β 2 < 1. Moreover, the dynamics exhibits aging at these time scales with a time-time correlation function converging to the arcsine law of this α-stable subordinator. In other words, up to rescaling, on these time scales (that are shorter than the equilibration time of the system) the dynamics of p-spin models ages in the same way as the REM, and by extension Bouchaud’s REM-like trap model, confirming the latter as a universal aging mechanism for a wide range of systems. The SK model (the case p = 2) seems to belong to a different universality class.

Stationary-increment student and variance-gamma processes

Abstract: A continuous-time model with stationary increments for asset price {Pt} is an extension of the symmetric subordinator model of Heyde (1999), and allows for skewness of returns. In the setting of independent variance-gamma-distributed returns the model resembles closely that of Madan, Carr, and Chang (1998). A simple choice of parameters renders {e_rr Pt} a familiar martingale. We then specify the activity time process, {Tt}, for which [Tt ? t] is asymptotically self-similar and [xt}, with zt = Tt ? 7}_i, is gamma distributed. This results in a skew variance-gamma distribution for each log price increment (return) Xt and a model for {Xt} which incorporates long-range dependence in squared returns. Our approach mirrors that for the (symmetric) Student process model of Heyde and Leonenko (2005), to which the present work is intended as a complement and a sequel. One intention is to compare, partly on the basis of fitting to data, versions of the general model wherein the returns have either (symmetric) t-distributions or variance-gamma distributions.