Fluctuation Theory for Upwards Skip-Free Lévy Chains
AbstractA fluctuation theory and, in particular, a theory of scale functions is developed for upwards skip-free Lévy chains, i.e., for right-continuous random walks embedded into continuous time as compound Poisson processes. This is done by analogy to the spectrally negative class of Lévy processes—several results, however, can be made more explicit/exhaustive in the compound Poisson setting. Importantly, the scale functions admit a linear recursion, of constant order when the support of the jump measure is bounded, by means of which they can be calculated—some examples are presented. An application to the modeling of an insurance company’s aggregate capital process is briefly considered. View Full-Text
Share & Cite This Article
Vidmar, M. Fluctuation Theory for Upwards Skip-Free Lévy Chains. Risks 2018, 6, 102.
Vidmar M. Fluctuation Theory for Upwards Skip-Free Lévy Chains. Risks. 2018; 6(3):102.Chicago/Turabian Style
Vidmar, Matija. 2018. "Fluctuation Theory for Upwards Skip-Free Lévy Chains." Risks 6, no. 3: 102.
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.