Development of hybrid six-stage bonus malus and deductible model for fair medical and health insurance premium rating / Rabi’atul’adawiyah Abdul Razak

This research delves into the application of a Bonus Malus System (BMS) within the sphere of medical and health insurance, focusing on three principal objectives. Firstly, the study endeavours to estimate claims numbers and sizes by elucidating the most appropriate methods for premium and claim estimations. Secondly, it proposes a hybrid premium system, integrating Bonus Malus and Stop-Loss elements, to refine the precision of premium calculations in the healthcare insurance domain. Lastly, the research seeks to validate the efficacy of time-discrete Markov chain models in the context of this hybrid system. The implementation of this hybrid system is anticipated to yield a mutually beneficial outcome for both insurance companies and policyholders. For insurers, it presents an effective means of curtailing fraudulent claims, while for the insured, it shields policyholders from penalties arising from legitimate claims. This study employs Markov Chain transition models to discern the scale for the Bonus Malus System. The anticipated claim amount and frequency data for this paper were sourced from the Society of Actuaries’ Project Oversight Group (POG) research project titled "Group Medical Insurance Large Claims Database Collection and Analysis" and simulated using Monte Carlo simulation in Excel. The study adopts a rigorous methodology comprising five distinct phases. Phase 1 involves controlling claim numbers and sizes, laying the groundwork for subsequent analyses. Phase 2 focuses on calculating premium income using the Bonus Malus System, while Phase 3 determines the optimal percentage for reward (bonus) and penalty (malus) within the BMS model. Phase 4 introduces simulations to ascertain the appropriate deductible amounts imposed on policies. Finally, Phase 5 concludes the methodology by estimating Medical and Health Insurance (MHI) premiums using the developed hybrid model. Through these comprehensive phases, a 6-stage BMS model is utilized, with a highest 40 percent reward (bonus) and a minimum 5 percent penalty (malus) applied to the base premium, favouring the -1/top scale for its simplicity, transparency, and consistency in penalty assessment. This study reveals that insured individuals with lower deductible amounts face a higher probability of being penalized compared to those with higher deductibles. The average deductible generated in this study ranges from $3,164.50 to $7,984.30, falling within the $9,100 maximum limit stipulated by the Affordable Care Act (ACA). Consequently, an additional premium top-up is suggested to maintain a stable risk pool, deemed essential for the sustained viability of an insurance company, beyond merely covering deductibles. The findings showed, the structured premium adjustments based on policyholders' claims history, combined with the Bonus Malus System (BMS) and deductibles, ensure predictability, transparency, and risk-based pricing. This approach fosters a balanced risk pool, stabilizes premiums by curbing small claims, and promotes customer engagement. The hybrid model's estimation of Medical and Health Insurance (MHI) premiums integrates these features, providing insurers with a flexible and comprehensive framework. This innovative approach reflects the industry's commitment to transparency, risk management, and customer-centric practices in shaping the future of medical insurance.