Affine Storage and Insurance Risk Models

Onno Boxma () and Michel Mandjes ()
Additional contact information
Onno Boxma: Department of Mathematics and Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven; Netherlands
Michel Mandjes: Korteweg-de Vries Institute for Mathematics, University of Amsterdam, 1098 XH Amsterdam, Netherlands

Mathematics of Operations Research, 2021, vol. 46, issue 4, 1282-1302

Abstract: The aim of this paper is to analyze a general class of storage processes, in which the rate at which the storage level increases or decreases is assumed to be an affine function of the current storage level, and, in addition, both upward and downward jumps are allowed. To do so, we first focus on a related insurance risk model, for which we determine the ruin probability at an exponentially distributed epoch jointly with the corresponding undershoot and overshoot, given that the capital level at time 0 is exponentially distributed as well. The obtained results for this insurance risk model can be translated in terms of two types of storage models, in one of those two cases by exploiting a duality relation. Many well-studied models are shown to be special cases of our insurance risk and storage models. We conclude by showing how the exponentiality assumptions can be greatly relaxed.

Keywords: Primary: 60K25; secondary: 90B15; Primary: Financial institutions/insurance/inventory and production/stochastic models/queues/transient results; storage processes; insurance risk models (search for similar items in EconPapers)
Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
http://dx.doi.org/10.1287/moor.2020.1097 (application/pdf)

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:inm:ormoor:v:46:y:2021:i:4:p:1282-1302

Access Statistics for this article

More articles in Mathematics of Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().