The Løkka–Zervos Alternative for a Cramér–Lundberg Process with Exponential Jumps

Florin Avram, Dan Goreac and Jean-François Renaud
Additional contact information
Florin Avram: Laboratoire de Mathématiques Appliquées, Université de Pau, 64012 Pau, France
Dan Goreac: School of Mathematics and Statistics, Shandong University, Weihai 264209, China
Jean-François Renaud: Département de Mathématiques, Université du Québec à Montréal (UQAM), Montréal, QC H2X 3Y7, Canada

Risks, 2019, vol. 7, issue 4, 1-9

Abstract: In this paper, we study a stochastic control problem faced by an insurance company allowed to pay out dividends and make capital injections. As in (Løkka and Zervos (2008); Lindensjö and Lindskog (2019)), for a Brownian motion risk process, and in Zhu and Yang (2016), for diffusion processes, we will show that the so-called Løkka–Zervos alternative also holds true in the case of a Cramér–Lundberg risk process with exponential claims. More specifically, we show that: if the cost of capital injections is low , then according to a double-barrier strategy, it is optimal to pay dividends and inject capital, meaning ruin never occurs; and if the cost of capital injections is high , then according to a single-barrier strategy, it is optimal to pay dividends and never inject capital, meaning ruin occurs at the first passage below zero.

Keywords: stochastic control; optimal dividends; capital injections; bankruptcy; barrier strategies; reflection and absorption; scale functions (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://www.mdpi.com/2227-9091/7/4/120/pdf (application/pdf)
https://www.mdpi.com/2227-9091/7/4/120/ (text/html)

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:gam:jrisks:v:7:y:2019:i:4:p:120-:d:296153

Access Statistics for this article

Risks is currently edited by Mr. Claude Zhang

More articles in Risks from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().