Robust reinsurance contract with learning and ambiguity aversion

Abstract

We investigate the robust reinsurance demand and price under learning and ambiguity aversion. In the reinsurance contract, the insurer is ambiguity neutral and believes that he is perfectly informed, and the reinsurer is a Bayesian learner and is aware that even the filtered model is the best description of the data-generating process, might not forecast the future claims correctly. The ambiguity-averse reinsurer has a preference for reinsurance contract which is robust to model misspecification. Closed-form expressions for the robust reinsurance demand and price are derived. We find that both the reinsurer's one-sided learning and ambiguity aversion influence the structures and levels of the optimal reinsurance demand and price. Moreover, if the ambiguity-averse reinsurer specifies the suboptimal reinsurance contract as an ambiguity-neutral decision-maker, it will result in significant utility loss and the utility loss increases with ambiguity aversion level and Bayesian volatility.

Keywords:

• Proportional reinsurance contract
• learning
• ambiguity
• robustness
• utility loss

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 The relative entropy between the distorted model and the reference model is defined as the expectation of the log Radon–Nikodym derivation under probability measure Q, which measures the distance between models Q and P. It can be shown that the relative entropy from time t to $t+\mathrm{\Delta }t$ is $\frac{1}{2}\phi (t{)}^2\mathrm{d}t$.

2 Schlesinger & Schulenburg 1991 and Seog 2002 point out that repeated purchasing behavior and multi-phase contracts make it common for the differential pricing of insurance products.

3 The principal-agent model in this paper is essentially a Stackelberg game, in which the reinsurer is the leader and the insurer is the follower.

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].