Reinsurance contract design with heterogeneous beliefs and learning

Abstract

We examine a continuous-time reinsurance contracting problem, where the reinsurer (principal) and the insurer (agent) disagree about the resolution of claim process. We illustrate the reinsurance contract design in an application with Bayesian learning. In the principal–agent framework, the reinsurer dynamically decreases the equilibrium reinsurance price instead of keeping it a constant. However, the reinsurance price increases about the belief differences. Both of these two opposite effects on the reinsurance price induce the insurer’s demand for reinsurance to first increase and then decrease with respect to decision time as the belief differences increase. Moreover, disagreement results in the relatively pessimistic insurer’s risk-taking behavior by raising risk retention as claim volatility increases. Furthermore, we find that when the belief differences are not too large, the reinsurer with belief differences and learning obtains greater satisfaction than the standard one.

Keywords:

• Principal-agent model
• proportional reinsurance contract
• learning
• disagreement

Notes

1 There also exist other methods to price risk. Jiang, Yuen, and Chen (2017) use the claim arrival rate to restrict the reinsurance price. Li et al. (2021) assume that the market price of risk depends on a Markovian, affine-form and square-root stochastic factor process.

Additional information

Funding

This research was supported by Natural Science Foundation of China [Grant No. 72161027] and Humanities and Social Science Research Foundation of Ministry of Education of China [Grant No. 19YJC790037].