2024/12/02 by David Landriault, Shi, Ziyue, Fangda Liu +2
Economics, Econometrics and Finance · Social Sciences · #FOS: Economics and business #Insurance and Financial Risk Management #Insurance, Mortality, Demography, Risk Management #Risk Management (q-fin.RM)
paper · pdf · doi:10.48550/arxiv.2412.01704
openalex publication_date 2024/12/02 · openalex created_date 2024/12/05 · openalex updated_date 2026/07/28
In the literature, insurance and reinsurance pricing is typically determined by a premium principle, characterized by a risk measure that reflects the policy seller's risk attitude. Building on the work of Meyers (1980) and Chen et al. (2016), we propose a new performance-based variable premium scheme for reinsurance policies, where the premium depends on both the distribution of the ceded loss and the actual realized loss. Under this scheme, the insurer and the reinsurer face a random premium at the beginning of the policy period. Based on the realized loss, the premium is adjusted into either a ''reward'' or ''penalty'' scenario, resulting in a discount or surcharge at the end of the policy period. We characterize the optimal reinsurance policy from the insurer's perspective under this new variable premium scheme. In addition, we formulate a Bowley optimization problem between the insurer and the monopoly reinsurer. Numerical examples demonstrate that, compared to the expected-value premium principle, the reinsurer prefers the variable premium scheme as it reduces the reinsurer's total risk exposure.