Refracted Levy processes


Kyprianou, A. E. and Loeffen, R. L., 2010. Refracted Levy processes. Annales De L Institut Henri Poincare-Probabilites Et Statistiques, 46 (1), pp. 24-44.

Related documents:

This repository does not currently have the full-text of this item.
You may be able to access a copy if URLs are provided below. (Contact Author)

Official URL:

Related URLs:


Motivated by classical considerations from risk theory, we investigate boundary crossing problems for refracted Levy processes. The latter is a Levy process whose dynamics change by subtracting off a fixed linear drift (of suitable size) whenever the aggregate process is above a pre-specified level. More formally, whenever it exists, a refracted Levy process is described by the unique strong solution to the stochastic differential equation dU(t) = -delta 1({Ut > b})dt + dX(t), where X = {X-t: t >= 0) is a Levy process with law P and b, delta is an element of R such that the resulting process U may visit the half line (b, infinity) with positive probability. We consider in particular the case that X is spectrally negative and establish a suite of identities for the case of one and two sided exit problems. All identities can be written in terms of the q-scale function of the driving Levy process and its perturbed version describing motion above the level b. We remark on a number of applications of the obtained identities to (controlled) insurance risk processes.


Item Type Articles
CreatorsKyprianou, A. E.and Loeffen, R. L.
Related URLs
Uncontrolled Keywordslevy processes,stochastic control,fluctuation theory
DepartmentsFaculty of Science > Mathematical Sciences
Research Centres
ID Code21613


Actions (login required)

View Item