Subordinator

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

Marshall-Olkin Distributions, Subordinators, Efficient Simulation, and Applications to Credit Risk

Abstract: The paper presents a novel construction of Marshall-Olkin (MO) multivariate exponential distributions of failure times as distributions of the first passage times of the coordinates of multidimensional Levy subordinator processes above independent unit-mean exponential random variables. A time-inhomogeneous version is also given that replaces Levy subordinators with additive subordinators. An attractive feature of MO distributions for applications, such as to portfolio credit risk, is its singular component that yields positive probabilities of simultaneous defaults of multiple obligors, capturing the default clustering phenomenon. The drawback of the original MO fatal shock construction of MO distributions is that it requires one to simulate 2n-1 independent exponential random variables. In practice, the dimensionality is typically on the order of hundreds or thousands of obligors in a large credit portfolio, rendering the MO fatal shock construction infeasible to simulate. The subordinator construction reduces the problem of simulating a rich subclass of MO distributions to simulating an n-dimensional subordinator. When one works with the class of subordinators constructed from independent one-dimensional subordinators with known transition distributions, such as gamma and inverse Gaussian, or their Sato versions in the additive case, the simulation effort is linear in n. To illustrate, the paper presents a simulation of 100,000 samples of a credit portfolio with 1,000 obligors that takes less than 18 seconds on a PC.

A Gamma Activity Time Process with Noninteger Parameter and Self-Similar Limit

Abstract: We construct a process with gamma increments, which has a given convex autocorrelation function and asymptotically a self-similar limit. This construction validates the use of long-range dependent t and variance-gamma subordinator models for actual financial data as advocated in Heyde and Leonenko (2005) and Finlay and Seneta (2006), in that it allows for noninteger-valued model parameters to occur as found empirically by data fitting.

On additive time-changes of Feller processes

Abstract: In this note we generalise the Phillips theorem [1] on the subordination of Feller processes by Levy subordinators to the class of additive subordinators (i.e. subordinators with independent but possibly nonstationary increments). In the case where the original Feller process is Levy we also express the timedependent characteristics of the subordinated process in terms of the characteristics of the Levy process and the additive subordinator.

Slow points and fast points of local times

Abstract: Let $L$ be a local time. It is well known that there exist a law of the iterated logarithm and a modulus of continuity for $L$. Motivated by the case of real Brownian motion, we study the existence of fast points and slow points of $L$. We prove the existence of such points by considering the right-continuous inverse of $L$, which is a subordinator.