Optimal Dividend, Reinsurance, and Capital Injection for Collaborating Business Lines under Model Uncertainty

2026-03-26

AI Summary

This study addresses the joint optimal strategy problem for a dual-line insurer under model uncertainty, integrating dividend payments, reinsurance, and capital injections. Accounting for heterogeneous ambiguity aversion across business lines, the surplus dynamics are modeled via diffusion processes, and a max-min framework is employed to jointly maximize the weighted expected discounted dividends while penalizing worst-case model misspecification. By leveraging stochastic dynamic programming and the associated Hamilton–Jacobi–Bellman (HJB) equation, the authors derive—within a multi-line collaborative setting featuring heterogeneous ambiguity aversion—the first closed-form equilibrium strategies: the optimal dividend-injection policy follows a barrier-type structure, while both the reinsurance proportion and the degree of model distortion decrease monotonically with total reserves. Numerical experiments confirm the sensitivity of these strategies to key parameters and highlight the significant impact of ambiguity aversion on optimal decision-making.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

This paper considers an insurer with two collaborating business lines that faces three critical decisions: (1) dividend payout, (2) reinsurance coverage, and (3) capital injection between the lines, in the presence of model uncertainty. The insurer considers the reference model to be an approximation of the true model, and each line has its own robustness preference. The reserve level of each line is modeled using a diffusion process. The objective is to obtain a robust strategy that maximizes the expected weighted sum of discounted dividends until the first ruin time, while incorporating a penalty term for the distortion between the reference and alternative models in the worst-case scenario. We completely solve this problem and obtain the value function and optimal (equilibrium) strategies in closed form. We show that the optimal dividend-capital injection strategy is a barrier strategy. The optimal proportion of risk ceded to the reinsurer and the deviation of the worst-case model from the reference model are decreasing with respect to the aggregate reserve level. Finally, numerical examples are presented to show the impact of the model parameters and ambiguity aversion on the optimal strategies.

Problem

• model uncertainty
• dividend
• reinsurance
• capital injection
• collaborating business lines

Innovation

• model uncertainty
• robust control
• barrier strategy
• diffusion process
• capital injection