Emerging risks are a significant concern in the insurance sector due to their complexity in assessment and coverage using traditional insurance mechanisms. Recent studies suggest that index-based insurance holds promise in mitigating emerging risks. This insurance model operates by using predefined indices that trigger the compensation process and determine the compensation amount without prior knowledge of actual losses. The simplified application of index-based insurance reduces costs and delays associated with indemnity-based insurance expertise. However, despite its benefits, index-based insurance encounters challenges in addressing severe losses, leading to increased basis risk. This issue is particularly pronounced in heavy-tailed losses, common in cyber insurance and insurance against natural disasters. This paper explores the optimal combination of index-based insurance with indemnity-based insurance contracts to leverage the strengths of both approaches. A threshold is introduced to determine when the different types of guarantees activate. Our theoretical and practical analyses contribute to designing this coverage by optimizing the policyholder’s utility. We validate our findings using real data from agricultural and cyber insurance contexts. The adopted model could facilitate discussions and create a consensus between insurers and insured around index-based solutions.
