On the area in the red of Lévy risk processes and related quantities

Mohamed Amine Lkabous and Zijia Wang

Insurance: Mathematics and Economics, 2023, vol. 111, issue C, 257-278

Abstract: Under contemporary insurance regulatory frameworks, an insolvent insurer placed in receivership may have the option of rehabilitation, during which a plan is devised to resolve the insurer's difficulties. The regulator and receiver must analyze the company's financial condition and determine whether a rehabilitation is likely to be successful or if its problems are so severe that the appropriate action is to liquidate the insurer. Therefore, it is essential to evaluate the cost required to support the insurer during its insolvent states in the decision-making process. To this end, we study areas in the red (below level 0) up to the recovery time, Poissonian, and continuous first passage times in this paper. Furthermore, we extend the study to the areas associated with Parisian ruin to evaluate the total cost until possible liquidation. For spectrally negative Lévy processes (SNLPs), also known as Lévy risk models, we derive the expectations of these quantities in terms of the well-known scale functions. Our results improve the existing literature, in which only expected areas for the Brownian motion and the Cramér-Lundberg risk process with exponential jumps are known.

Keywords: Cost of recovery; Area in the red; Lévy risk processes (search for similar items in EconPapers)
JEL-codes: C02 C46 G22 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167668723000434
Full text for ScienceDirect subscribers only

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:eee:insuma:v:111:y:2023:i:c:p:257-278

DOI: 10.1016/j.insmatheco.2023.05.005

Access Statistics for this article

Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu

More articles in Insurance: Mathematics and Economics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().