Fluctuation Theory for Upwards Skip-Free Lévy Chains

Autor:	Matija Vidmar
Jazyk:	angličtina
Rok vydání:	2018
Předmět:	Lévy processes non-random overshoots skip-free random walks fluctuation theory scale functions capital surplus process Insurance HG8011-9999
Zdroj:	Risks, Vol 6, Iss 3, p 102 (2018)
Druh dokumentu:	article
ISSN:	2227-9091
DOI:	10.3390/risks6030102
Popis:	A 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.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/961fd8acb58e4c08b47d7de4cbda839b Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
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