The Design of Optimal Re-Insurance Contracts when Losses are Clustered
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912535385473024 |
|---|---|
| author | Bernis, Guillaume Di Girolami, Cristina Scotti, Simone |
| author_facet | Bernis, Guillaume Di Girolami, Cristina Scotti, Simone |
| contents | This paper investigates the form of optimal reinsurance contracts in the case of clusters of losses. The underlying insured risk is represented by a marked Hawkes process, where the intensity of the jumps depends not only on the occurrence of previous jumps but also on the size of the jumps, which represents the financial magnitude of the loss. The reinsurance contracts are applied to each loss at the time of occurrence, but their structure is assumed to be constant. We derive closed-form formulas within the meanvariance framework. Additionally, we demonstrate that the optimal contract is not the classical excess-loss (deductible) form. The optimal contract is piecewise linear with three ranges: first, no reinsurance below a certain threshold; second, reinsurance with a slope greater than 1; and finally, full reinsurance. When the marked process converges to a Poisson process, we recover the optimality of the deductible form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02624 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Design of Optimal Re-Insurance Contracts when Losses are Clustered Bernis, Guillaume Di Girolami, Cristina Scotti, Simone Optimization and Control 91G05, 60G55 This paper investigates the form of optimal reinsurance contracts in the case of clusters of losses. The underlying insured risk is represented by a marked Hawkes process, where the intensity of the jumps depends not only on the occurrence of previous jumps but also on the size of the jumps, which represents the financial magnitude of the loss. The reinsurance contracts are applied to each loss at the time of occurrence, but their structure is assumed to be constant. We derive closed-form formulas within the meanvariance framework. Additionally, we demonstrate that the optimal contract is not the classical excess-loss (deductible) form. The optimal contract is piecewise linear with three ranges: first, no reinsurance below a certain threshold; second, reinsurance with a slope greater than 1; and finally, full reinsurance. When the marked process converges to a Poisson process, we recover the optimality of the deductible form. |
| title | The Design of Optimal Re-Insurance Contracts when Losses are Clustered |
| topic | Optimization and Control 91G05, 60G55 |
| url | https://arxiv.org/abs/2508.02624 |