Abstract:
Kenyan insurance firms have introduced insurance policies of chronic illnesses
like cancer; however, they have faced a huge challenge in the pricing of
these policies as cancer can transit into different stages, which consequently
leads to variation in the cost of treatment. This has made the estimation of
aggregate losses of diseases which have multiple stages of transitions such as
cancer, an area of interest of many insurance firms. Mixture phase type distributions
can be used to solve this setback as they can in-cooperate the transition
in the estimation of claim frequency while also in-cooperating the heterogeneity
aspect of claim data. In this paper, we estimate the aggregate losses
of secondary cancer cases in Kenya using mixture phase type Poisson Lindley
distributions. Phase type (PH) distributions for one and two parameter Poisson
Lindley are developed as well their compound distributions. The matrix
parameters of the PH distributions are estimated using continuous Chapman
Kolmogorov equations as the disease process of cancer is continuous while
severity is modeled using Pareto, Generalized Pareto and Weibull distributions.
This study shows that aggregate losses for Kenyan data are best estimated
using PH-OPPL-Weibull model in the case of PH-OPPL distribution
models and PH-TPPL-Generalized Pareto model in the case of PH-TPPL distribution
models. Comparing the two best models, PH-OPPL-Weibull model
provided the best fit for secondary cancer cases in Kenya. This model is also
recommended for different diseases which are dynamic in nature like cancer.
