The following is an excellent post by Brian Lenehan at Asteron on why people tend to buy life insurance - even though it is not such a good 'bet' than, say, medical or disability insurance. I particularly appreciate the theory of risk that peopleare prepared to take small losses - but not large ones. This helps explain at the same stroke both why life insurance is preferred, and disability or medical not so. First, here is the question I posted:
Why don't people insure what's important? Let me give you an example: they insure their lives with greater frequency than they insure either their health or income. Given the greater probability of an insurable event, and the fact that the latter two have worse claims rates (meaning insurers pay out a greater proportion of the premium in claims) they are clearly the better deal.
In simple terms my humble Lidunian view it is a matter of perceived value relative to actual value. Goods can be compared and ranked according to which good provides the most utility which is what perceived value broadly represents. The second related reason is that the shape of the utility curve varies. For large losses people are risk averse and for small losses people are more likely to be risk takers (this also explains why we have gambling and insurance)
When we spoke I said I remembered a paper by Rose Friedman related to this. Well my memory failed me as the paper was by Milton Friedman and Savage (see references below). By the way Friedman (like Warren Buffett aspired to be an actuary in his youth)
Actual value and perceived value often vary. There are some studies (http://research.nottingham.ac.uk/NewsReviews/newsDisplay.aspx?id=145serach) which show people generally underestimate their life expectancy (they overestimate their mortality risk) and as such the perceived value of life insurance may be higher than the actual value. Other things being equal these leads risk averse people to seek out life insurance which they see as having a high perceived value.
I am not aware of whether people underestimate or overestimate morbidity risk (covered by health / income insurance). If one sets as an hypothesis that morbidity risk is underestimated then health / income insurance will have a perceived value less than the actual value.
So there we have it - higher perceived value relative to actual value (reflected in price) leads to higher demand.
A second explanation relates to utility theory. This is of course the whole basis of insurance. Without wishing to teach you to suck eggs the theory is that individuals may be risk averse and as such insurance allows them to maximize their utility by reducing risk. That is simple enough. Further studies (starting off which the Friedman / Savagae paper) show that people are both risk averse and risk takers along different parts of the curve (risk averse for large losses and risk takers for small losses). Friedman / savage used this to explain by people have demand for both insurance and gambling. Insurance (in particular life insurance) relates to the risk of a large loss (economic loss of death). For large losses individuals were shown to be risk averse and this leads to the demand for insurance. Gambling involves the probability of a small loss countered by a small chance of large gain. Friedman / savage argued that for small losses individuals are risk-takers and this leads to a demand for gambling.
Now back to your point. Both life and income protection insurance generally cover a large potential loss and for this individuals are supposedly risk averse. This means individuals should rationally purchase life and income insurance.
Health insurance is (generally) covering smaller cover levels. Following on the logic this involves a relatively small potential loss and the individual is less risk averse and potentially more risk-taking. As such the need for health insurance (in terms of a rational person maximizing utility) could be rationally explained as being less than for life and income insurance.
Eden, Benjamin: 1977, The role of insurance and gambling in allocating risk over time , Journal of Economic Theory 16, 228–246.
Friedman, Milton and Savage, Leonard J.: 1942, The utility analysis of choices involving risk , Journal of Political Economy 56, 279–301.
Friend, Irwin and Blume, Marshall E.: 1975, The demand for risky assets , American Economic Review 65, 900–922.
Markowitz, H.: 1952, The utility of wealth , Journal of Political Economy 60, 151–158.
Szpiro, George G.: 1986, Measuring risk aversion: an alternative approach , Review of Economics and Statistics 68, 156–159.
Szpiro, George G.: 1987, The decision to buy or sell insurance under constant relative risk aversion, The Geneva Papers on Risk and Insurance 12, 34–36.
Friedman, Milton and Savage, Leonard J.: 1942, The utility analysis of choices involving risk , Journal of Political Economy 56, 279–301