Cancer insurance pricing under different scenarios associated with diagnosis and treatment

We consider pricing of a specialised critical illness and life insurance contract for breast cancer (BC) risk. We compare (a) an industry-based Markov model with (b) a recently developed semi-Markov model, which accounts for unobserved BC cases and progression through clinical stages of BC, and (c) an alternative Markov model derived from (b). All models are calibrated using population data in England and data from the medical literature. We show that the semi-Markov model aligns best with empirical evidence. We then consider net premiums of specialized life insurance products under various scenarios of cancer diagnosis and treatment. The results show strong dependence on the time spent with diagnosed or undiagnosed pre-metastatic BC. This proves to be significant for refining cancer survival estimates and accurately estimating related age dependence by cancer stage. In contrast, the industry-based model, by overlooking this critical factor, is more sensitive to the model assumptions, underscoring its limitations in cancer estimates.