Academic journal article Journal of Risk and Insurance

Aspects of Optimal Multiperiod Life Insurance

Academic journal article Journal of Risk and Insurance

Aspects of Optimal Multiperiod Life Insurance

Article excerpt

Aspects of Optimal Multiperiod Life Insurance


A multiperiod model is used to analyze aspects of whole life and term insurance contracts within the context of the lifetime consumption-investment problem. Not only the life status, but also the state of health of the consumer is considered in examining optimal insurance purchases. Particular attention is given to the policy loan and guaranteed reinsurability options of the whole life insurance contract. When viewed in this context, whole life insurance, term insurance, and savings are shown likely to coexist in an optimal consumption-investment plan rather than act as substitutes for each other. In this paper it is shown how the bounds of the insurance pricing parameters can be derived to ensure that both kinds of insurance will continue to be sought by rational consumers, while avoiding adverse selection and lapsation.


Over the past three decades there has been a conundrum in the economic and business literature. Why do so many people purchase whole life insurance when it has been shown that a combination of term insurance and savings dominates a whole life policy? Equally puzzling is that many people hold both (individual or group) term life and whole life insurance. Are consumers irrational or simply poorly informed?

This article demonstrates that rational, well-informed consumers will choose to hold both term and whole life policies. This result is achieved by considering aspects of whole life insurance which have heretofore escaped formal modeling--features which render the whole life contract distinguishable from linear combinations of term life insurance and a savings program. The simultaneous demand for both kinds of insurance is shown to occur under standard actuarial pricing practices, both with actuarially fair pricing and with typical premium loadings.

This article comes at a juncture characterized by a pause in the demand for whole life insurance. During the past variations of life insurance (e.g., universal life) and new investment vehicles (e.g., interest rate options), which effectively unbundle features of the whole life policy that had rendered it unique, were actively marketed. Consequently, consumers have been afforded the opportunity of seeking only those policy options they deem useful while avoiding payment for the others.

The past several years have raised doubts, however, that these newer insurance policies will ever return a profit to insurers, notwiethstanding a remarkable consumer demand for them. Actuaries claim the problem lies in pricing that is so competitive as to preclude their ability to properly charge for the options granted policyholders. While this situation cannot persist in the long run, it has created a strong desire among some insurers to be more circumspect in the kinds and amounts of policies they write. Many insurers are returning to more traditional products, where the bundling together of options leaves them less susceptible to simultaneous utilization. Most have attempted to offer revised policy provisions in their old book of business that strip the policies of some of their more troublesome options. For example, consumers can opt for a revised contract with a variable-rate policy loan feature and in return receive higher dividends or cash value crediting rates reflecting their utilization of policy loans. Some newly offered whole life policies feature dual premium schedules--a low-premium schedule for insureds who periodically provide evidence of insurability and another rate for those who do not provide such evidence. Other policies link the cash value accumulation patterns to actual market values of the assets supporting these policies.

Most of the innovations in life insurance policies sold today represent some combination of elements in the traditional whole life policy with term insurance and/or a variable savings program. …

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