Irreversible reinsurance: A singular control approach

Tingjin Yan, Kyunghyun Park and Hoi Ying Wong

Insurance: Mathematics and Economics, 2022, vol. 107, issue C, 326-348

Abstract: Reinsurance demand is often investigated using the classical stochastic control framework with the reinsurance level as a regular control variable. However, reinsurance contracts are not traded, and dynamic adjustment of the reinsurance strategy is impractically infeasible. Moreover, reinsurance contracts are long-term commitments and are considered irreversible as they are expensive to close before maturity. We propose a novel irreversible reinsurance framework, where the insurer enters into a sequence of reinsurance contracts at the most appropriate times and the contracts are never reversed afterwards. In each contract, the insurer specifies the amount of reinsurance. We model the insurer's risk exposure using a mean-reverting process as inspired by stochastic mortality modeling and the property loss data from US catastrophes, and then formulate the reinsurance decision as a two-dimensional degenerate singular control problem. Our mathematical problem is closely related to the well-known finite-fuel problem due to the boundedness of the insurer's risk retention. The optimal reinsurance purchase rule is triggered by a free boundary that characterizes the optimal relationship between risk exposure and reinsurance demand. We conduct a numerical analysis to investigate the features of the singular reinsurance strategy and its dependency on the model parameters.

Keywords: Dynamic reinsurance; Singular control; Skorokhod reflection; Mean-reverting risk exposure; Free boundary (search for similar items in EconPapers)
JEL-codes: C61 G22 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167668722001068
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:107:y:2022:i:c:p:326-348

DOI: 10.1016/j.insmatheco.2022.09.004

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 ().