Stackelberg equilibrium reinsurance contract with smooth ambiguity under thinning-dependence framework

Yu Yuan, Kam Chuen Yuen and Fudong Wang

Scandinavian Actuarial Journal, 2025, vol. 2025, issue 10, 959-988

Abstract: In this paper, we design the optimal reinsurance contract for the insurer and reinsurer with thinning-dependent insurance businesses in the Stackelberg differential game. The ambiguity-neutral insurer plays the role of follower and aims to determine an optimal per-loss reinsurance strategy for each line of insurance business. The reinsurer plays as the role of leader and looks for the reinsurance premium under the average performance. Different from the existing work, the reinsurer has her own insurance business, which is also correlated with the reinsurance businesses. Because of the nonlinear term due to smooth ambiguity, we are confronted with a time-inconsistent optimization problem. The semi-explicit expressions for the optimal reinsurance and premium controls as well as the value functions of both parties are derived under the time-consistent framework. We find that considering the smooth ambiguity is equivalent to changing the distribution of the uncertain parameter with the Esscher transform. Also, the reinsurer's own business has a significant impact on the optimal reinsurance premium loading. Finally, some numerical examples are provided to illustrate the influence of model parameters on the contract as well as the economic interpretation behind.

Date: 2025
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DOI: 10.1080/03461238.2025.2488341

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