Studies on life insurance consumption dates back to Heubner (1942) who postulated that human life value has certain qualitative aspects that gives rise to its economic value. But his idea was normative in nature as it suggested ‘how much’ of life insurance to be purchased and not ‘what’ will be purchased. There were no guidelines regarding the kind of life policies to be selected depending upon the consumers capacity and the amount of risk to be carried in the product.
Economic value judgments are made on both the normative as well as positive issues. Later studies on insurance gradually incorporated these issues via assimilating developments in the field of risk and uncertainty following works by von Neumann and Morgenstern (1947), Arrow (1953), Debreu (1953) and others. The economics on insurance demand became more focused on evaluating the amount of risk to be shared between the insured and the insurer rather than evaluation of life or property values. This emerged because it was risk associated with individual life or property that called for an economic valuation of the cost of providing insurance.
Life insurance is essentially a form of saving, competing with other forms of saving in the market. The theory of life insurance demand thus developed through the life-cycle model(s) of saving. Let a person’s income rate and his consumption plan are represented by a continuous function of time and respectively. Thus, net saving (positive or negative) at time t is given by
--- (1)
where, δ is the rate of interest.
Even though all individuals want to consume as much possible, this does not happen in reality and the above expression of saving is constrained by number of possibilities. For example, the person has no debt [ ], solvent at time of his death at time T [ ] and leaves a bequest of amount B [ ].
Uncertainty associated with time of death is represented by a random variable with density , where is the probability that a person at age x shall still be alive after a time t. Taking expectation of (1) and discontinuing, we get
--- (2)
--- (3)
If the individual takes pure endowment insurance, single premium being
,
Thus, net saving equals .
This shows that saving through life insurance takes place at a higher rate of interest than conventional saving. In the determination of optimal insurance consumption, the conventional utilitarian theory is adopted which reflects individuals preferences over different consumption patterns. Let us consider the utility function of the form
--- (4)
where, β is the ‘impatience’ to consume.
Assuming the person had no debt at time T i.e., , the problem is to maximize its utility (4). The solution gives us, . Within this framework, various forms of life insurance are introduced; the probability associated with death or number of maximum life years is considered; and then the expected utility of consumption is maximized subject to any one of the three restrictions on the net savings as described above.
The role of insurance in the above model has been predominantly to smoothen out consumption over time, make bequests, and repay debts or to insure a constant income stream after retirement. The ongoing discussion also reveals that individuals’ current income and future anticipated consumption expenditure plays a crucial role in determining the amount of insurance purchased (we are, for a while ignoring the form in which insurance is purchased).
The importance of rate of interest (δ) or the impatience factor (β) is also worth considering. Preferences over different consumption pattern vary from person to person and there are ‘qualitative’ factors which affects such preferences.
Using the expected utility framework in a continuous time model, Yaari (1965) studied the problem of uncertain lifetime and life insurance. Including the risk of dying in the life cycle model, he showed conceptually that an individual increases expected lifetime utility by purchasing fair life insurance and fair annuities. Simple models of insurance demand were proposed by Pratt (1964), Mossin (1969), Smith (1968) and others; considering a risk averse decision maker with an initial wealth W.
The results indicate that demand for life insurance varies inversely with the wealth of the individuals. Hakansson (1969) used a discrete-time model of demand for financial assets and life insurance purchase in particular to examine bequest motive in considerable detail. Pissarides (1980) further extending Yaari’s work proved that life insurance was theoretically capable of absorbing all fluctuations in lifetime income. Lewis (1989) found out that the number of dependents as an influence on the demand for life insurance.
To sum up, the theoretical review yields macroeconomic variables like income, rate of interest, and accumulated savings in wealth form; along with a set of demographic or social variables having potential impact on an individuals’ decision to opt for or not to demand life insurance. Life insurance consumption increases with the breadwinner’s probability of death, the present level of family’s consumption and the degree of risk aversion.
Economic value judgments are made on both the normative as well as positive issues. Later studies on insurance gradually incorporated these issues via assimilating developments in the field of risk and uncertainty following works by von Neumann and Morgenstern (1947), Arrow (1953), Debreu (1953) and others. The economics on insurance demand became more focused on evaluating the amount of risk to be shared between the insured and the insurer rather than evaluation of life or property values. This emerged because it was risk associated with individual life or property that called for an economic valuation of the cost of providing insurance.
Life insurance is essentially a form of saving, competing with other forms of saving in the market. The theory of life insurance demand thus developed through the life-cycle model(s) of saving. Let a person’s income rate and his consumption plan are represented by a continuous function of time and respectively. Thus, net saving (positive or negative) at time t is given by
--- (1)
where, δ is the rate of interest.
Even though all individuals want to consume as much possible, this does not happen in reality and the above expression of saving is constrained by number of possibilities. For example, the person has no debt [ ], solvent at time of his death at time T [ ] and leaves a bequest of amount B [ ].
Uncertainty associated with time of death is represented by a random variable with density , where is the probability that a person at age x shall still be alive after a time t. Taking expectation of (1) and discontinuing, we get
--- (2)
--- (3)
If the individual takes pure endowment insurance, single premium being
,
Thus, net saving equals .
This shows that saving through life insurance takes place at a higher rate of interest than conventional saving. In the determination of optimal insurance consumption, the conventional utilitarian theory is adopted which reflects individuals preferences over different consumption patterns. Let us consider the utility function of the form
--- (4)
where, β is the ‘impatience’ to consume.
Assuming the person had no debt at time T i.e., , the problem is to maximize its utility (4). The solution gives us, . Within this framework, various forms of life insurance are introduced; the probability associated with death or number of maximum life years is considered; and then the expected utility of consumption is maximized subject to any one of the three restrictions on the net savings as described above.
The role of insurance in the above model has been predominantly to smoothen out consumption over time, make bequests, and repay debts or to insure a constant income stream after retirement. The ongoing discussion also reveals that individuals’ current income and future anticipated consumption expenditure plays a crucial role in determining the amount of insurance purchased (we are, for a while ignoring the form in which insurance is purchased).
The importance of rate of interest (δ) or the impatience factor (β) is also worth considering. Preferences over different consumption pattern vary from person to person and there are ‘qualitative’ factors which affects such preferences.
Using the expected utility framework in a continuous time model, Yaari (1965) studied the problem of uncertain lifetime and life insurance. Including the risk of dying in the life cycle model, he showed conceptually that an individual increases expected lifetime utility by purchasing fair life insurance and fair annuities. Simple models of insurance demand were proposed by Pratt (1964), Mossin (1969), Smith (1968) and others; considering a risk averse decision maker with an initial wealth W.
The results indicate that demand for life insurance varies inversely with the wealth of the individuals. Hakansson (1969) used a discrete-time model of demand for financial assets and life insurance purchase in particular to examine bequest motive in considerable detail. Pissarides (1980) further extending Yaari’s work proved that life insurance was theoretically capable of absorbing all fluctuations in lifetime income. Lewis (1989) found out that the number of dependents as an influence on the demand for life insurance.
To sum up, the theoretical review yields macroeconomic variables like income, rate of interest, and accumulated savings in wealth form; along with a set of demographic or social variables having potential impact on an individuals’ decision to opt for or not to demand life insurance. Life insurance consumption increases with the breadwinner’s probability of death, the present level of family’s consumption and the degree of risk aversion.