Optimal Dividend, Reinsurance, and Capital Injection Strategies for an Insurer with Two Collaborating Business Lines
This paper analyzes a bivariate optimal dividend problem for an insurer with two collaborating business lines under a diffusion model with correlated Brownian motions. The framework incorporates dividend payouts, proportional reinsurance, and inter-line capital transfers to prevent bankruptcy. The authors provide complete analytical solutions, identifying three scenarios with closed-form value functions and optimal strategies. Results show a threshold dividend policy, with the more important line having a lower threshold. Optimal reinsurance decreases with aggregate reserves and stabilizes after a switching point. Correlation between lines affects reinsurance, and the capital transfer rule is consistent across scenarios.