In this paper we consider pricing of insurance contracts for breast cancer risk based on three multiple state models. Using population data in England and data from the medical literature, we calibrate a collection of semi-Markov and Markov models. Considering an industry-based Markov model as a baseline model, we demonstrate the strengths of a more detailed model while showing the importance of accounting for duration dependence in transition rates. We quantify age-specific cancer incidence and cancer survival by stage along with type-specific mortality rates based on the semi-Markov model which accounts for unobserved breast cancer cases and progression through breast cancer stages. Using the developed models, we obtain actuarial net premiums for a specialised critical illness and life insurance product. Our analysis shows that the semi-Markov model leads to results aligned with empirical evidence. Our findings point out the importance of accounting for the time spent with diagnosed or undiagnosed pre-metastatic breast cancer in actuarial applications.

翻译：本文基于三种多重状态模型，探讨乳腺癌风险的保险合同定价问题。利用英格兰人口数据及医学文献资料，我们校准了一系列半马尔可夫和马尔可夫模型。以行业标准的马尔可夫模型作为基准模型，我们展示了更精细模型在考虑转移率持续时间依赖性方面的重要性。我们基于半马尔可夫模型（该模型考虑了未观测到的乳腺癌病例及乳腺癌分期进展）量化了分阶段的特定年龄癌症发病率与癌症生存率，以及特定类型的死亡率。利用所建立的模型，我们计算了专业重大疾病和人寿保险产品的精算纯保费。分析表明，半马尔可夫模型得出的结果与实证证据一致。我们的研究结果指出了在精算应用中考虑已诊断或未诊断的癌前转移乳腺癌所经历时间的重要性。