On loss-sensitive rating plans

Loss-Sensitive Rating Plans involve risk sharing between insurers and insured, providing mutual benefits such as loss control incentives. Unlike guaranteed-cost policies, these plans incorporate a variable premium component dependent on the insured's loss experience. This paper proposes a formalization of insurance premiums under retrospective rating and large deductible plans, offering a generalized approach. In retrospective rating, premiums adjust based on claims within the policy period, while large deductible plans entail fixed premiums with unknown actual costs below the deductible. The insurer's liability may be capped, but the insured's exposure remains unlimited. We introduce representations of insurer and insured burdens, emphasizing the importance of minimum and maximum premiums and adherence to the balance principle. Various mathematical formulations and properties are discussed, offering insights into premium calculation methodologies. This study underscores the need for other robust premium calculation criteria beyond mean values, ensuring risk-sharing practices between insurers and insured.