guarantee that the income continues for life, the insurance company relies on a concept called cross-subsidy or the "law of large numbers". Because an annuity population can be expected to have a distribution of lifespans around the population's mean (average) age, those dying earlier will give up income to support those living longer whose money would otherwise run out. Thus it is a form of longevity insurance (see also below). A life annuity, ideally, can reduce the "problem" faced by a person when they don't know how long they will live, and so they don't know the optimal speed at which to spend their savings. Life annuities with payments indexed to the Consumer Price Index might be an acceptable solution to this problem, but there is only a thin market for them in North America. Life annuity variants For an additional expense (either by way of an increase in payments (premium) or a decrease in benefits), an annuity or benefit rider can be purchased on another life such as a spouse, family member or friend for the duration of whose life the annuity is wholly or partly guaranteed. For example, it is common to buy an annuity which will continue to pay out to the spouse of the annuitant after death, for so long as the spouse survives. The annuity paid to the spouse is called a reversionary annuity or survivorship annuity. However, if the annuitant is in good health, it may be more advantageous to select the higher payout option on his or her life only and purchase a life insurance policy that would pay income to the survivor. The pure life annuity can have harsh consequences for the annuitant who dies before recovering his or her investment in the contract. Such a situation, called a forfeiture, can be mitigated by the addition of a period-certain feature under which the annuity issuer is required to make annuity payments for at least a certain number of years; if the annuitant outlives the specified period certain, annuity payments continue until the annuitant's death, and if the annuitant dies before the expiration of the period certain, the annuitant's estate or beneficiary is entitled to the remaining payments certain. The tradeoff between the pure life annuity and the life-with-period-certain annuity is that the annuity payment for the latter is smaller. A viable alternative to the life-with-period-certain annuity is to purchase a single-premium life