Subordinator

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

Asymptotic behaviour of first passage time distributions for subordinators

Abstract: In this paper we establish local estimates for the first passage time of a subordinator under the assumption that it belongs to the Feller class, either at zero or infinity, having as a particular case the subordinators which are in the domain of attraction of a stable distribution, either at zero or infinity. To derive these results we first obtain uniform local esti mates for the one dimensional distribution of such a subordinator, which sharpen those obtained by Jain and Pruitt [8]. In the particular case of a subordinator in the domain of attraction of a stable distribution our results are the analogue of the results obtained by the authors in [6] for non-monotone Levy processes. For subordinators an approach different to that in [6] is necessary because the excursion techniques are not available and also because typically in the non-monotone case the tail distribution of the first passage time has polynomial decrease, while in the subordinator case it is exponential.

A risky asset model based on Lévy processes and asymptotically self-similar activity time processes with long-range dependence

Abstract: In the paper, using Levy processes subordinated by ‘asymptotically self-similar activity time’ processes with long-range dependence, we set up new asset pricing models. Using the different construction for gamma (Γ) based ‘asymptotically self-similar activity time’ processes with long-range dependence from Finlay and Seneta (2006) we extend the constructions for inverse-gamma and gamma based ‘asymptotically selfsimilar activity time’ processes with integer-valued parameters and long-range dependence in Heyde and Leonenko (2005) and Finlay and Seneta (2006) to noninteger-valued parameters.

Tempered fractional Cauchy problems on bounded domains

Abstract: This paper develops strong solutions and stochastic solutions for the tempered fractional diffusion equation on bounded domains. First the eigenvalue problem for tempered fractional derivatives is solved. Then a separation of variables, and eigenfunction expansions in time and space, are used to write strong solutions. Finally, stochastic solutions are written in terms of an inverse subordinator.

Limiting behaviour of the stationary search cost distribution driven by a generalized gamma process

Abstract: Consider a list of labeled objects that are organized in a heap. At each time, object $j$ is selected with probability $p_j$ and moved to the top of the heap. This procedure defines a Markov chain on the set of permutations which is referred to in the literature as Move-to-Front rule. The present contribution focuses on the stationary search cost, namely the position of the requested item in the heap when the Markov chain is in equilibrium. We consider the scenario where the number of objects is infinite and the probabilities $p_j$’s are defined as the normalization of the increments of a subordinator. In this setting, we provide an exact formula for the moments of any order of the stationary search cost distribution. We illustrate the new findings in the case of a generalized gamma subordinator and deal with an extension to the two–parameter Poisson–Dirichlet process, also known as Pitman–Yor process.

Levy subordinator model: A two parameter model of default dependency

Abstract: The May 2005 crisis and the recent credit crisis have indicated to us that any realistic model of default dependency needs to account for at least two risk factors, firm-specific and catastrophic. Unfortunately, the popular Gaussian copula model has no identifiable support to either of these. In this article, a two parameter model of default dependency based on the Levy subordinator is presented accounting for these two risk factors. Subordinators are Levy processes with non-decreasing sample paths. They help ensure that the loss process is non-decreasing leading to a promising class of dynamic models. The simplest subordinator is the Levy subordinator, a maximally skewed stable process with index of stability 1/2. Interestingly, this simplest subordinator turns out to be the appropriate choice as the basic process in modeling default dependency. Its attractive feature is that it admits a closed form expression for its distribution function. This helps in automatic calibration to individual hazard rate curves and efficient pricing with Fast Fourier Transform techniques. It is structured similar to the one-factor Gaussian copula model and can easily be implemented within the framework of the existing infrastructure. As it turns out, the Gaussian copula model can itself be recast into this framework highlighting its limitations. The model can also be investigated numerically with a Monte Carlo simulation algorithm. It admits a tractable framework of random recovery. It is investigated numerically and the implied base correlations are presented over a wide range of its parameters. The investigation also demonstrates its ability to generate reasonable hedge ratios.