Ruin probabilities for a Lévy-driven generalised Ornstein–Uhlenbeck process

Yuri Kabanov () and Serguei Pergamenshchikov ()
Additional contact information
Yuri Kabanov: Université de Franche-Comté
Serguei Pergamenshchikov: Université de Rouen
Authors registered in the RePEc Author Service: Юрий Михайлович Кабанов

Finance and Stochastics, 2020, vol. 24, issue 1, No 2, 39-69

Abstract: Abstract We study the asymptotics of the ruin probability for a process which is the solution of a linear SDE defined by a pair of independent Lévy processes. Our main interest is a model describing the evolution of the capital reserve of an insurance company selling annuities and investing in a risky asset. Let β>0$\beta >0$ be the root of the cumulant-generating function H$H$ of the increment V1$V_{1}$ of the log-price process. We show that the ruin probability admits the exact asymptotic Cu−β$Cu^{-\beta }$ as the initial capital u→∞$u\to \infty $, assuming only that the law of VT$V_{T}$ is non-arithmetic without any further assumptions on the price process.

Keywords: Ruin probabilities; Dual models; Price process; Renewal theory; Distributional equation; Autoregression with random coefficients; Lévy process; 60G51 (search for similar items in EconPapers)
JEL-codes: G22 G23 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://link.springer.com/10.1007/s00780-019-00413-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:finsto:v:24:y:2020:i:1:d:10.1007_s00780-019-00413-3

Ordering information: This journal article can be ordered from
http://www.springer. ... ance/journal/780/PS2

DOI: 10.1007/s00780-019-00413-3

Access Statistics for this article

Finance and Stochastics is currently edited by M. Schweizer

More articles in Finance and Stochastics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().