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臺大管理論叢
第
27
卷第
2S
期
239
model can determine the frequency and cost of medical services (Duan et al., 1983; Keeler
and Rolph, 1988; Mullahy, 1998; Deb and Trivedi, 2002; Frees et al., 2011). The collective
risk model constructs predictions for both the claim number and the claim size in actuarial
mathematics, using compound Poisson processes, mixed Poisson processes, and so forth.
The Markov process model is another technique to price a lifetime disability or medical
insurance (Hoem, 1988; Wolthuis, 2003; Stenberg et al., 2007; D’Amico et al., 2009).
According to the cancer morbidity data and the cost of per physician visit obtained by using
the NHIRD, this study adopts a collective risk model to construct a lifetime cancer insurance
pricing model.
The collective risk model needs to determine the distributions of both claim number and
claim size. In order to fit the data appropriately, we test three discrete type distributions: a
zero-truncated Poisson distribution (ZTPO), a zero-truncated negative binominal distribution
(ZTNB), and a geometric distribution (Geo). Moreover, this study uses maximal likelihood
estimation (MLE) to estimate the parameters of these three discrete type distributions.
Furthermore, in order to deal with the trade-off between the goodness of fit of the
distribution and the complexity of the distribution, we evaluate the Akaike information
criterion (AIC) and the Bayesian information criterion (BIC). From the results of an analysis
comparing the MLE, AIC, and BIC statistics, this study concludes that the ZTNB fits the
cancer morbidity and the cost of per physician visit better than the other two distributions.
Finally, by using the probability generating function of insurance benefit with respect to the
insured’s age, we find the fair premium explicitly.
In conclusion, the findings of this study show that cancer morbidity among the younger
generation has increased greatly from 1996 to 2011, and the average insurance benefit of
patients per physician visit was stable in the last decade. The numerical results also indicate
that the continued treatment rate and the medical cost increases with age, and the older
generation have a higher insurance benefit. In addition, our study demonstrates that the
premium increase is a result of a continuous increase in cancer morbidity, especially in the
younger generation. Furthermore, our study also shows that the maximum difference
premium cost has reached nearly 60 percent for males and 35 percent for females from 1998
to 2003.