Subordinator

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

Mixtures of Tempered Stable Subordinators

Abstract: In this article, we introduce mixtures of tempered stable subordinators (TSS). These mixtures define a class of subordinators which generalize tempered stable subordinators. The main properties like probability density function (pdf), Levy density, moments, governing Fokker-Planck-Kolmogorov (FPK) type equations, asymptotic form of potential density and asymptotic form of the renewal function for the corresponding inverse subordinator are discussed. We also generalize these results to n-th order mixtures of TSS.

Semi-implicit Euler-Maruyama method for non-linear time-changed stochastic differential equations.

Abstract: The semi-implicit Euler-Maruyama (EM) method is investigated to approximate a class of time-changed stochastic differential equations, whose drift coefficient can grow super-linearly and diffusion coefficient obeys the global Lipschitz condition. The strong convergence of the semi-implicit EM is proved and the convergence rate is discussed. When the Bernstein function of the inverse subordinator (time-change) is regularly varying at zero, we establish the mean square polynomial stability of the underlying equations. In addition, the numerical method is proved to be able to preserve such an asymptotic property. Numerical simulations are presented to demonstrate the theoretical results.

Pricing Industry Loss Warranties in a Lévy-Frailty Framework

Abstract: We propose a novel risk-neutral pricing approach for industry loss warranties In doing so, we explicitly take into account the statistical dependence of the losses on individual policies in the underlying insurance portfolio, caused by the occurrence of a natural catastrophe Inspired by recent advances in the structured credit literature, we model joint claim events in a Levy–Frailty framework with a stochastic time change Event time is driven by rare and large jumps of a compound Poisson subordinator and thus elapses more quickly when a natural catastrophe has struck, leading to a clustering of losses We estimate the model on historical ILW quotes and obtain encouraging fit statistics

On moments and tail behaviors of storage processes

Abstract: We study the existence of moments and the tail behaviour of the densities of storage processes. We give sufficient conditions for existence and non-existence of moments using the integrability conditions of submultiplicative functions with respect to Levy measures. Then, we study the asymptotical behavior of the tails of these processes using the concave or convex envelope of the release rate function.

Weak Subordination of Multivariate L\'evy Processes

Abstract: Subordinating a multivariate L\'evy process, the subordinate, with a univariate subordinator gives rise to a pathwise construction of a new L\'evy process provided the subordinator and the subordinate are independent processes. The Variance Gamma model in finance was generated accordingly from a Brownian motion and a Gamma process. Alternatively, multivariate subordination can be used to create L\'evy processes, but this requires the subordinate to have independent or indistinguishable components. In this paper, we show that there exists another operation acting on pairs (T,X) of L\'evy processes which creates a L\'evy process X \.o T. Here, T is a subordinator, but X is an arbitrary L\'evy process with possibly dependent coordinates. We show that this method is an extension of both univariate and multivariate subordination and provide two applications. Firstly, we give a weak formulation of the Variance-alpha-Gamma-process that exhibits a wider range of dependence than using traditional subordination, and fit this model to a S&P500-FTSE100 data set. Secondly, the Variance Generalised Gamma Convolution class of L\'evy processes formed by subordinating Brownian motion with Thorin subordinators is further extended using weak subordination.