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Optimal reinsurance contract in a Stackelberg game framework: a view of social planner

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  • Xia Han
  • David Landriault
  • Danping Li

Abstract

In this paper, we consider an optimal reinsurance contract under a mean-variance criterion in a Stackelberg game theoretical framework. The reinsurer is the leader of the game and decides on an optimal reinsurance premium to charge, while the insurer is the follower of the game and chooses an optimal per-loss reinsurance to purchase. The objective of the insurer is to maximize a given mean-variance criterion, while the reinsurer adopts the role of social planner balancing its own interests with those of the insurer. That is, we assume that the reinsurer determines the reinsurance premium by maximizing a weighted sum of the insurer's and reinsurer's mean-variance criteria. Under the general mean-variance premium principle, we derive the optimal reinsurance contract by solving the extended Hamilton–Jacobi–Bellman (HJB) systems. Moreover, we provide an intuitive way to set the weight of each party in the reinsurer's objective. Finally, we consider some special cases to illustrate our main results.

Suggested Citation

  • Xia Han & David Landriault & Danping Li, 2024. "Optimal reinsurance contract in a Stackelberg game framework: a view of social planner," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2024(2), pages 124-148, February.
  • Handle: RePEc:taf:sactxx:v:2024:y:2024:i:2:p:124-148
    DOI: 10.1080/03461238.2023.2220219
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