Continuous-time optimal reporting with full insurance under the mean-variance criterion

Jingyi Cao, Dongchen Li, Virginia R. Young and Bin Zou

Insurance: Mathematics and Economics, 2025, vol. 120, issue C, 79-90

Abstract: We study a continuous-time, loss-reporting problem for an insured with full insurance under the mean-variance (MV) criterion. When a loss occurs, the insured faces two options: she can report it to the insurer for full reimbursement but will pay a higher premium rate; or she can hide it from the insurer by paying it herself and enjoy a lower premium rate. The insured follows a barrier strategy for loss reporting and seeks an optimal barrier to maximize her MV preferences over a random horizon. We show that this problem yields an optimal barrier that is not necessarily decreasing with respect to the insured's risk aversion, as intuition suggests it should. To address this non-monotonicity, we propose two solutions: in the first solution, we restrict the feasible strategies to a bounded interval; in the second, we modify the MV criterion by replacing the variance of the insured's wealth with the variance of the insured's retained losses. We obtain the optimal barrier strategy in semiclosed form—as a unique positive zero of a nonlinear function—for both modified models, and we show that it is a decreasing function of the insured's risk aversion, as expected.

Keywords: Barrier strategies; Insurance; Loss reporting; Mean-variance (search for similar items in EconPapers)
JEL-codes: C61 G22 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167668724001094
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:120:y:2025:i:c:p:79-90

DOI: 10.1016/j.insmatheco.2024.11.004

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 ().