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Some actuarial aspects of health insurance

Rickayzen, B. D. (2007). Some actuarial aspects of health insurance. (Unpublished Doctoral thesis, City, University of London)


The thesis demonstrates some ways in which multiple state models can be used to investigate particular actuarial aspects of two common health insurance products: income protection (IP) insurance and long term care (LTC) insurance. The thesis contains 4 papers: two concerning IP insurance and two concerning LTC insurance.

The first paper investigates the sensitivity of IP insurance premiums to changes in the parameter values used in a multiple state model. Lapses are incorporated within the model, and the net premium for a particular policy is tested for sensitivity to the various parameters used, including their interaction with the lapse rate. One of the conclusions is that the net premium is insensitive to changes in the lapse rate.

The main objective of the second paper is to measure the process error for a portfolio of independent IP insurance policies in a multiple state modelling context. A second objective is to observe the extent to which the process error changes as we increase the volatility and complexity of the models which generate investment returns and inflation.

The results demonstrate that pooling, as implied by the law of large numbers, reduces the process error. However, once we introduce volatility to the investment and inflation experience, we find that the economic process risk is considerably more significant than the demographic process risk.

In the third paper, a multiple state model is developed to project, over the next 35 years, the number of people in the United Kingdom with different levels of disability. These projections assist in identifying the potential demand for LTC by the older population in the future. The projections suggest that the resource implications of having an ageing population in the UK will be ameliorated by a reduction, over the projection period, in the proportion of older people who are severely disabled.

The fourth paper uses the multiple state model described in the third paper to investigate a potential new type of LTC product: a disability-linked annuity. The annuity is purchased while the individual is in reasonable health, and the level of payment is increased as the individual becomes more disabled. The product is analysed under various health scenarios and using different definitions of disability. The premium is compared with that required for the corresponding standard annuity (which does not increase upon the onset of disability). It is found that, given the additional disability benefits provided by the product, the increase in premium required is relatively modest. It is therefore potentially an attractive product, albeit only affordable by the more affluent section of the population.

The overall conclusion of the thesis is that multiple state models have a significant part to play in health insurance in terms of both calculating premiums and reserves, and in measuring risk. Hence, the use of multiple state models should be viewed as being an important technique by health insurance actuaries when considering the broad array of risk management tools at their disposal.

Publication Type: Thesis (Doctoral)
Subjects: H Social Sciences > HA Statistics
H Social Sciences > HF Commerce
Departments: Bayes Business School > Actuarial Science & Insurance
Bayes Business School > Bayes Business School Doctoral Theses
Doctoral Theses
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