Optimal Dividend, Reinsurance and Capital Injection Strategies for Collaborating Business Lines: The Case of Excess-of-Loss Reinsurance

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Autori principali: Boonen, Tim J., Vega, Engel John C. Dela
Natura: Preprint
Pubblicazione: 2025
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author Boonen, Tim J.
Vega, Engel John C. Dela
author_facet Boonen, Tim J.
Vega, Engel John C. Dela
contents This paper considers an insurer with two collaborating business lines that must make three critical decisions: (1) dividend payout, (2) a combination of proportional and excess-of-loss reinsurance coverage, and (3) capital injection between the lines. The reserve level of each line is modeled using a diffusion approximation, with the insurer's objective being to maximize the weighted total discounted dividends paid until the first ruin time. We obtain the value function and the optimal strategies in closed form. We then prove that the optimal dividend payout strategy for bounded dividend rates is of threshold type, while for unbounded dividend rates it is of barrier type. The optimal combination of proportional and excess-of-loss reinsurance is shown to be pure excess-of-loss reinsurance. We also show that the optimal level of risk ceded to the reinsurer decreases as the aggregate reserve level increases. The optimal capital injection strategy involves transferring reserves to prevent the ruin of one line. Finally, numerical examples are presented to illustrate these optimal strategies.
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id arxiv_https___arxiv_org_abs_2511_11383
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Optimal Dividend, Reinsurance and Capital Injection Strategies for Collaborating Business Lines: The Case of Excess-of-Loss Reinsurance
Boonen, Tim J.
Vega, Engel John C. Dela
Optimization and Control
Mathematical Finance
Risk Management
91G05 (Primary) 93E20 (Secondary)
This paper considers an insurer with two collaborating business lines that must make three critical decisions: (1) dividend payout, (2) a combination of proportional and excess-of-loss reinsurance coverage, and (3) capital injection between the lines. The reserve level of each line is modeled using a diffusion approximation, with the insurer's objective being to maximize the weighted total discounted dividends paid until the first ruin time. We obtain the value function and the optimal strategies in closed form. We then prove that the optimal dividend payout strategy for bounded dividend rates is of threshold type, while for unbounded dividend rates it is of barrier type. The optimal combination of proportional and excess-of-loss reinsurance is shown to be pure excess-of-loss reinsurance. We also show that the optimal level of risk ceded to the reinsurer decreases as the aggregate reserve level increases. The optimal capital injection strategy involves transferring reserves to prevent the ruin of one line. Finally, numerical examples are presented to illustrate these optimal strategies.
title Optimal Dividend, Reinsurance and Capital Injection Strategies for Collaborating Business Lines: The Case of Excess-of-Loss Reinsurance
topic Optimization and Control
Mathematical Finance
Risk Management
91G05 (Primary) 93E20 (Secondary)
url https://arxiv.org/abs/2511.11383