Subordinator

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

On the inverse gamma subordinator

Abstract: In this paper we deal with some open problems concerned with Gamma subordinators. In particular, we first provide a representation for the moments of the inverse gamma subordinator. Then, we focus on λ-potentials and we study the governing equations associated with Gamma subordinators and inverse processes. Such representations are given in terms of higher transcendental functions, also known as Volterra functions.

A Jump Ornstein–Uhlenbeck Bridge Based on Energy-Optimal Control and Its Self-Exciting Extension

Abstract: We study a version of the Ornstein-Uhlenbeck bridge driven by a spectrally-positive subordinator. Our formulation is based on a Linear-Quadratic control subject to a singular terminal condition. The Ornstein-Uhlenbeck bridge, we develop, is written as a limit of the obtained optimally controlled processes, and is shown to admit an explicit expression. Its extension with self-excitement is also considered. The terminal condition is confirmed to be satisfied by the obtained process both analytically and numerically. The methods are also applied to a streamflow regulation problem using a real-life dataset.

Inflation derivatives modelling using time changed Levy processes

Abstract: This paper considers inflation derivatives modelling by using the time changed Levy processes of Carr and Wu (2004), in a Heath- Jarrow-Morton framework. By applying the results in Andersen (2008), we derive drift conditions for nominal and real forward rates and zero coupon bonds. Similarly a drift condition for the consumer price in- dex is found. We show how to price standard inflation derivatives by considering a complex (time dependent) measure as in Carr and Wu (2004). By specifying the subordinator as a generalized affine process, the prices of these derivatives can be obtained up to ordinary differ- ential equations and possibly Fourier inversion. Finally we calibrate our model to market data. Our results show that even though Levy processes can improve the fit to data, an investigation in the exact specification of the Levy process and volatility loading is still needed.

On subordinate random walks

Abstract: In this article subordination of random walks in $R^d$ is considered. We prove that subordination of random walks in the sense of [BSC12] yields the same process as subordination of Levy processes (in the sense of Bochner). Furthermore, we prove that appropriately scaled subordinate random walk converges to a multiple of a rotationally $2\alpha$-stable process if and only if the Laplace exponent of the corresponding subordinator varies regularly at zero with index $\alpha\in (0,1]$.