Lapse-supported pricing: Is it worth the risks?

March 8, 2004 (original: September 19, 2000)

"Unexpected Rate Rises Jolt Elders Insured For Long-Term Care" the June 22, 2000 edition of The Wall Street Journal reported on the front page. On one level, this is a story about seniors who bought long term care insurance from two companies, Conseco and Penn Treaty, and who now feel betrayed. They thought that their premiums would stay the same for life, but unexpected rate increases have left them with no good options. They can’t afford the higher premiums, and they can’t shop for new coverage because they are no longer insurable. So they’ll have to drop the policies and lose everything they have paid so far, or they’ll have to come up with more money for premiums somehow. They bought long term care insurance for peace of mind, and now they’re in a financial mess.

But this story isn’t just about long term care insurance. It opens a window on a dangerous practice called lapse-supported pricing that puts millions of unaware insurance buyers at risk. Here is the key paragraph of the article:

"So why were the initial premiums so low that repeated increases were later necessary? The two insurers, which made big pushes into this business and quickly grabbed big chunks of it, deny intentionally underpricing policies to gain market share. They blame their own miscalculations. A key one was assuming that a substantial number of policyholders would change their minds and let their coverage lapse early on, thus ceasing to be a liability. Instead, 85% to 95% of customers renewed every year, creating an aging clientele that cost far more in claims than expected."

Three features of long term care insurance policies create the risk that premiums will increase even if the insurance company can accurately predict future health care costs:

  • There is a level premium, based on the issue age.
  • The level premium is not guaranteed. The company has the right to raise rates for all policyholders as a group.
  • There are no cash values or other benefits if you drop the policy. You lose everything that you have paid.

A level premium is designed to make insurance affordable for life. You pay more than the expected cost of health care claims during the early years, and the insurance company builds up an internal fund to cover the higher cost of claims in the later years. When you drop the policy, you forfeit your share of that internal fund. The company expects that each year some people will decide to drop their policies, and it takes this into account when it determines what the level premium should be for everyone. The money left behind by people who leave lets the company charge everyone a lower premium than it would if it paid the terminators their share of the internal fund. If fewer people leave than the company estimated, it can raise the premiums for those who remain.

This pricing scheme is used for more than just long term care insurance. Many insurers rely on anticipated lapses to ensure the profitability of other types of policies, including:

  • guaranteed renewable, level premium disability income insurance
  • nonguaranteed, level premium term insurance
  • cash value life insurance with artificially low cash values in the early years and artificially low costs in the later years

For example, here’s a profit projection for a group of 30-year level premium term insurance policies that an actuary presented at an October 1998 meeting of the Society of Actuaries:

Present value of profits: 30-year term insurance
With assumed lapse ratesa $103,000
With no lapses $(942,000)
aAssumed rates in pricing: 12-15% in the first year, grading down to 5-8% over time.

If people drop their policies as the company expects, it will make $103,000, but if no one drops out, it will lose $942,000. Those losses will be the responsibility of a future generation of managers, after the current generation has retired or moved on to other companies. The future managers are the people who will decide if the company should raise rates to stop the flow of red ink.

So what?

Why should you care if a company uses lapse-supported pricing? You should care because lapse-supported pricing creates risks, and you can’t make an informed purchase decision without understanding those risks.

Let’s start with comments made by an actuary at a May 1991 meeting of the Society of Actuaries:

"When I first learned of these practices, I made a presentation to my boss to explain what lapse-supported pricing was. At the end of my presentation my boss looked at me and said, ‘Well? What are the actuaries going to do about this?’ It was totally natural, in his mind, that the actuaries, who have the control, would devise the solution.

And I had to tell him, ‘I’m not sure the actuaries are going to do anything about it because frankly, the people who are coming up with these schemes are probably getting big raises and nice promotions, and they don’t have much incentive to scale back.’ If sales are made based on the assumption that only 10% will be long-term persisters, the inevitable result is that 90% will be disappointed because they had intended to be part of the 10%.

A car salesman could not advertise a picture of a Lamborghini, and put it in a box, and then have customers come in and pay for the Lamborghini, only to realize later that only one out of ten buyers really got a Lamborghini, the other nine getting an old Nash or Volkswagen. They would have to disclose that it’s a lottery, and that if you are unlucky, you get the Nash. You have to be lucky and a survivor to get the Lamborghini."

Here are the problems with lapse-supported policies:

  • If you’re one of the people who gets out early — for whatever reason — you’ll be sorry that you bought the policy, because you will have overpaid for the coverage that you got. Everyone who buys a lapse-supported policy expects to keep it for a long time, but insurance companies know better. Their actual experience confirms that people regularly drop policies. Maybe they find a better-looking policy. Maybe they suffer a financial setback and can’t afford to pay premiums anymore. Maybe their insurance needs change. For whatever reason, some people who were confident that they would keep the policy change their minds later.
  • If fewer people drop out than the company expected, there won’t be enough money to maintain the low premiums for those who remain. The company has to make an assumption about lapse rates to price the policy, and that assumption may turn out to be wrong. With most policies, lower lapse rates can result in better values, because the company can spread its costs among more policies remaining on the books. With lapse-supported policies, lower lapse rates hurt long-term performance. If premiums are not guaranteed, the company’s executives can respond to the mounting losses by raising premiums.
  • Lapse-supported pricing can put all of a company’s policyholders at risk, not just those who bought the lapse-supported policies. If the company sells a lot of lapse-supported policies with guaranteed premiums and misjudges lapse rates, its financial condition could be seriously affected. It might then take money from other policyholders to make up for the losses on the lapse-supported policies. At the extreme, the company might be taken over by state regulators, and the guaranteed premiums on the lapse-supported policies might not be honored.
  • The growth of secondary markets where life insurance policies can be bought and sold will make it harder than ever for companies to predict lapse rates. Policies that used to lapse will stay on the books and merely change hands. Owners of lapse-supported policies may be able to sell them for considerably more than their cash value, but that also increases the pricing risk for the remaining policyholders.
  • The company may spend the internal fund instead of keeping it for the benefit of the loyal policyholders. Some companies use the early profits from lapses to pay dividends to their corporate parent, and it’s not clear where the money will come from to pay the attractive values being illustrated to the unsuspecting buyers. At worst, this can turn into a kind of Ponzi scheme: the company has to sell more and more lapse-supported policies to generate funds to cover the losses on the policies that were sold earlier.
  • A related problem is that lapse-supported pricing makes it harder to determine the quality of a company’s earnings. Is it a coincidence that one company that is in the process of demutualizing has developed a lapse-supported policy for use in shifting assets from qualified plans? Are the executives looking ahead to the nice stock options that they’ll have and trying to create an impressive income statement to pump up the stock?
  • Years from now, the company may decide not to redistribute the money that it has held back. Today’s management may be committed to paying everything that has been illustrated, but what about the executives who will be making decisions in the future? Won’t their compensation go up if they renege on the implicit contract that the company made years before with its policyholders? Or what if another company takes over the lapse-supported policies, through one of the many mergers and acquisitions that now occur in the financial services industry. Will it be as committed to fair treatment as the issuing company?
  • Lapse-supported pricing can create a perverse relationship between the company and its customers, because at some point the company may be better off if everyone drops their policies. This is hardly an incentive to treat policyholders well over the long run. The insurer–customer relationship is perverse in another way: the insurer knows its past, present and projected lapse rates, and the insurer controls pricing, but the customer bears the lapse risk.
  • Lapse-supported pricing can lead people to turn up their noses at policies that offer genuinely superior value, because they don’t understand that the lower illustrated price of a lapse-supported policy may be fool’s gold. The inability of consumers to distinguish between high-quality and low-quality policies creates an opportunity for unfair competition. Insurers with competitive advantages in distribution costs, investment performance, underwriting skill and other fundamentals can lose sales to insurers whose only competitive advantage is a greater willingness to rob Peter to pay Paul.
  • Lapse-supported pricing greatly complicates your decision about whether to keep or replace an existing policy, because the range of plausible future outcomes is much wider. If a non-lapse-supported policy is performing poorly, it is likely to continue performing poorly, and it can properly be replaced. What can you say if a lapse-supported policy is a poor value in the near term but looks like a good deal down the road? How do you make a judgment about the chances of long-term success?

In sum, lapse-supported pricing greatly increases the difficulty of making informed decisions, because the risks are not adequately disclosed and the procedures to ensure accountability are inadequate. It’s one thing to speculate with your eyes wide open, but it’s a safe bet that not one buyer in a hundred understands the risks involved in buying nonguaranteed, lapse-supported policies. They certainly don’t think of themselves as speculators, but that’s what they are. They are speculating on lapse rates and on the pricing decisions of future insurance company executives.

An analogy with overbooking

Comparison of overbooking by airlines and insurance companies
Airlines Insurance companies
Description Airlines sell tickets for more seats than are available on the flight, because they expect that some people won’t show up. Insurance companies collect premiums for benefits that they cannot afford to pay to everyone, because they expect that some people will drop their policies.
Do people understand? Yes. Most people know that airlines overbook. No. Very few people understand how insurance products are priced.
What happens if it doesn’t work as planned? The airline asks for volunteers to take a later flight and gives them a voucher worth hundreds of dollars. The insurance company points to the fine print in the contract and says that the policy will lapse if the higher premium isn’t paid.

A life insurance example

A client recently asked me for a second opinion on a proposal that she had received from a financial planner (a.k.a. insurance agent) for a $1 million life insurance policy. Here are the illustrated level premiums to endow at age 100 for the agent’s policy and a low-load policy:

Endowment level premiuma
Agent’s policy $27,460
Low-load policy $34,490
a$1,000,000 policy issued to 73-year-old woman

The agent’s policy pays a full commission, whereas the low-load policy has much lower sales costs because it is sold directly to the public without agents. This is reflected in the first-year cash surrender values: the agent’s policy has no first-year cash value (all of the premium is spent on commissions and other marketing costs), whereas the low-load policy has a first-year cash value of $29,350. There is no question that the agent’s policy has a significant competitive disadvantage in selling expense, which is one of the fundamental factors that determines policy cost. So why is the agent’s policy 20% cheaper than the low-load policy?

One reason is that the agent’s policy has a super-preferred underwriting class, which my client qualified for, whereas the low-load company does not distinguish between preferred and super-preferred. A reasonable estimate based upon the expected present value of death claims is that this difference in policy design might be worth up to 125% of the difference in selling costs. In other words, it could offset the higher selling costs, plus some. (To put it another way, most of the savings created by my client’s good health is squandered on marketing costs, and my client gets the remainder.) A generous estimate is that this could account for a 5% lower price.

Where does the rest of the difference come from? Let’s look at the load structure of both policies for clues. We know that the account value at the end of each year is simply equal to the account value at the beginning of the year, plus premiums, minus loads, plus interest. (To understand cash value life insurance, think of the mechanics of an interest-bearing checking account.) So if the low-load policy requires a $7,030 higher annual premium to grow to $1 million at age 100, there must be higher loads being deducted or lower interest being credited.

The low-load policy has no surrender charge, whereas the agent-sold policy has a $47,750 surrender charge in the first year, declining gradually over 20 years. However, the surrender charge is paid only by people who drop their policies, so that doesn’t explain why it takes an additional $7,030 each year in the low-load policy to reach $1 million at age 100.

The low-load policy has a 3.5% premium load to cover state and Federal premium sales taxes; the agent-sold policy has no premium load. Of course, both companies are subject to the same taxes; they are just charging for them in different ways.

The agent’s company charges a little more for policy administration ($6 a month versus $4 a month).

The low-load policy pays a 0.25% higher interest rate during the first nine years. The agent’s company increases the base interest rate by a nonguaranteed 0.25% in Year 10 (so it catches up with the low-load company’s rate) and another nonguaranteed 0.25% in Year 20 (so it exceeds the low-load company’s rate for the remaining eight years until age 100).

Taken together, these items do not come close to explaining a 20% difference in premiums.

There is one item left to consider: the cost-of-insurance (COI) charges that are deducted each month. These charges are typically expressed as a rate per $1,000 of insurance. Take a quick look at the table below, and then I’ll explain what we can learn from it.

Comparison of current annual cost-of-insurance rates
Agent’s company Low-load company
(1) (2) (3) (4)
Policy year Age COI As % of 1975-80 table COLI COI COI
1 73 13.83 287% 2.68 5.83
2 74 15.37 222 3.83 7.87
3 75 15.37 167 5.09 10.04
5 77 15.37 108 7.91 14.69
10 82 15.39 44 19.50 25.40
15 87 15.39 16 39.32 46.37
20 92 15.39 10 100.35 117.21
21 93 54.16 32 120.30 126.83
25 97 71.75 32 168.77 168.63
26 98 76.44 32 181.39 180.06

Column 1 shows the current (nonguaranteed) annual rate charged per $1,000 of net amount at risk — that is, the difference between the $1 million death benefit and the account value — for the agent’s policy. In the first year, if the average account value is about $22,000, the cost-of-insurance deductions would total about $13,500 (i.e., (1000–22) x 13.83). The COI rates are roughly level for the first 20 years (similar to 20-year level premium term insurance), and then they increase each year (similar to annual renewable term insurance).

Column 2 shows how these COI rates compare with mortality rates taken from the 1975-80 Unismoker Select & Ultimate Table. That table is based on the actual death claims experience of a large group of insurers, and it is often used as a benchmark by pricing actuaries. The mortality rates were measured from 1975 to 1980, and mortality has improved since then, so actuaries use a percentage of the 1975-80 table rates and also make adjustments for company-specific factors. (The Society of Actuaries has prepared an updated table based on 1990-95 experience, but the 1975-80 table is still used as a benchmark in practice.) A typical pricing assumption for super-preferred underwriting is that the probability of death (and therefore the cost of death claims per $1,000 at risk) will be about 30% of the 1975-80 table.

The COI rates are much greater than expected death rates during the early years. One reason is that the company uses the monthly COI charges to recoup commissions and other expenses in addition to the cost of death claims. That explains the high charge in the first year, and perhaps the second, but the company is certainly not incurring over $13,000 of expenses in each of the subsequent years. What is the company doing with the rest of the money that it deducts from the policy?

Column 2 shows that the COI rates gradually decline to only 10% of the 1975-80 table in Year 20. This is just a fraction of the expected cost of death claims. How is the company covering its costs at that point?

After Year 20, the COI rates are in line with expected death claims, with just a small margin for expenses and profit. There is disagreement among actuaries about whether it is reasonable to assume that super-preferred mortality rates will be consistently lower than standard rates throughout life; it is possible that super-preferred and standard rates will converge at advanced ages.

The agent’s company has a separate division that manufactures and sells low-load policies to large corporations and wealthy individuals. These sophisticated buyers often put multi-million-dollar premiums into these COLI (corporate-owned life insurance) policies. Column 3 shows the COI rates for several of the COLI products. These rates are for the best underwriting class, nonsmoker (there is no super-preferred). The rates were recently reduced, especially at older ages, based on the company’s updated mortality studies.

Unlike the retail COI rates, the COLI COI rates increase each year, similar to annual renewable term. The rates are about 55% of the 1975-80 table for the first 10 years and, with minor exceptions, gradually rise to 75% of the 1975-80 table at the highest ages. The company’s retail division and its COLI division appear to have a significant disagreement about the probability of death for nonagenarians. At age 92, the COLI division charges over six times as much as the retail division, and at ages 93 to 98 it charges over twice as much. These differences cannot be explained by the difference between standard and super-preferred underwriting criteria.

It’s worth noting that large corporations and wealthy individuals obviously have the right to buy the high-commission retail policy rather than the low-commission COLI policies, but the company’s wholesale division has not been driven out of business by the retail division.

The final column of the table (Column 4) shows the low-load company’s COI rates. They have the same pattern as the COLI COI rates, but they are generally higher, reflecting the higher marketing expenses in the retail versus large corporate market. Both companies’ rates are almost the same at advanced ages.

A comparison of Column 1 and Column 4 reveals that the COI rates of the agent’s policy are higher than the low-load company’s COI rates during the first few years, but they are significantly lower in the later years. This is the main reason why the agent’s illustrated premium is 20% less than the low-load premium.

So now we’re in a better position to make a conjecture about how the agent’s proposed policy works. The agent’s company pays out more money for commissions and other selling expenses than the low-load company does. It recovers those expenses through high cost-of-insurance charges and high surrender charges in the early years, and through a relatively high spread between what it earns on its investments and the interest rate that it credits to the policy. The insurance and surrender charges and the interest rate spread are actually higher than what the company needs for expenses and profit. It sets a portion of those charges aside in an unregulated internal fund to be used to boost the interest rate and reduce the insurance charges for the small number of policies that it expects to remain in force over the long term.

Lapse-supported pricing, combined with the use of a super-preferred underwriting class, allows the company to illustrate a premium that is 20% lower than the low-load company’s premium. If more people keep their policies in force than the actuaries expect, the company has the right to increase the cost-of-insurance charges, eliminate the interest rate bonus, or reduce the base interest rate. This is truly a "trust me" pricing scheme.

Is this conjecture correct? Let’s look at the Illustration Questionnaire, a disclosure document developed by the Society of Financial Service Professionals. Here’s the key question and the company’s complete answer:

Question V.1. If the actual persistency is better than that assumed, would that negatively affect illustrated values?

Answer: No.

It is well known that 20-year level premium term insurance is lapse-supported. This company is saying that when you put 20-year level premium term insurance inside a universal life policy, it somehow ceases to be lapse-supported.

Do you want to bet your financial security on that?

A brief history of lapse-supported pricing

Lapse-supported pricing is not new, and prudent insurance buyers won’t find comfort in its history.

We could begin in the fourteenth century, but let’s jump ahead to 1652. France needed money to start wars, and an Italian banker and promoter named Lorenzo Tonti proposed a solution. Citizens would buy shares in a government-run pool that would divide the investment earnings each year among the surviving participants. Decedents’ heirs would receive nothing, and when the last participant died, the principal would revert to the state. On paper, this arrangement could provide a handsome annuity to the lucky participants who enjoyed a long life.

Tonti’s proposal displayed the essential ingredients of a tontine, defined by Robert W. Cooper in a 1972 monograph as "a scheme whereby those members of a specified group who survive and/or persist receive a future benefit of an unknown amount at the expense of those members who die and/or withdraw from the group." Tontines can be distinguished from other insurance arrangements based on survivorship, such as life annuities, by the feature that the ultimate payouts are unknown.

Tonti’s idea gathered dust until 1670, when a small tontine was organized in the Netherlands. As decades passed, the actual annual payments to the participants were less than a fifth of what had been projected, because the annuitants lived much longer than expected.

The French government set up a much larger tontine in 1689. During the next 80 years, France and other European countries organized many variations with mixed success. For the state, tontines were a relatively easy way to borrow money. For the participants, they were sometimes viewed as an investment but were more often simply speculation. Inaccurate mortality forecasts were not the only risk; the terms of the contract were sometimes unilaterally changed by the issuers, resulting in severe losses for the income recipients.

In the United States, the history of tontines begins in 1867. The eight-year-old Equitable Life Assurance Society had depleted its capital to match the annual dividends of its competitors, and its survival was in jeopardy. To gain a competitive edge, The Equitable created a tontine policy that paid no dividends until the end of 10 to 20 years. Decedents forfeited their share of the surplus pool, and early terminators forfeited dividends and cash values. This allowed The Equitable to illustrate very large dividends to prospective buyers, while downplaying the reality that actual dividends would be subject to the discretion of the board of directors.

This combination of insurance, investment, and speculation was initially very popular, and most of The Equitable’s competitors quickly followed its lead. As the companies’ surplus grew, their marketing strategy shifted from competing for customers by providing high dividends to competing for agents by raising commissions.

Early enthusiasm for tontine policies turned to anger, however, as policyholders realized that they would forfeit everything if they dropped out and might lose even more by staying in. State legislatures investigated, but the insurance industry successfully lobbied against action. When policyholders turned to the courts for redress, they were rarely successful at getting contracts interpreted in their favor.

To deal with growing public dissatisfaction, insurance companies developed deferred dividend policies (also called semi-tontines) that provided cash surrender values, although all dividends would still be forfeited during the specified tontine period of five to 20 years. This adaptation worked, and sales continued to climb. Many companies found that semi-tontines were more popular than the much less speculative annual dividend policies, because they appealed to the public’s dual desires to insure and to gamble.

Semi-tontines led to even greater outrage, however, as actual experience emerged. Many policyholders received dividends that were less than half of what they had expected to get. Again, state legislatures and the courts offered little redress, until the New York legislature formed a committee — the Armstrong Committee — in 1905 to undertake a thorough investigation of the life insurance industry. Their report was presented in 1906, and it described mismanagement and corruption throughout the industry. Undistributed surplus that was supposedly being accumulated for the benefit of tontine and semi-tontine policyholders had been squandered on lavish payments to agents and company executives. This, plus lower interest rates and marketing-oriented illustrations, had produced the dividend shortfalls.

The Armstrong Committee traced many of the abuses to the lack of accountability in the management of the surplus funds. Because tontines and semi-tontines did not pay annual dividends, mismanagement could go undetected for many years. Therefore, one of the committee’s key recommendations was to require the payment of annual dividends, and this was soon adopted in New York and elsewhere.

Despite the scandals uncovered in the Armstrong investigation, policies with tontine and semi-tontine characteristics continued to be marketed by some companies in some states. Renewed warnings of potential sales abuses were made in trade publications and at industry conferences in the 1950s and 1960s.

As universal life became more popular in the 1980s, some companies used various types of persistency bonuses to make illustrated values look better. One technique was — and still is — to illustrate a higher interest rate after certain periods, such as 10 or 20 years. The actual cost may be small if few policies are still on the books, and the company retains the right to reduce the base interest rate to offset the bonus. These bonuses are difficult to analyze, because some of them are a legitimate way of reducing unneeded charges; that is, some bonuses are lapse-supported and some aren’t.

In 1995, the National Association of Insurance Commissioners adopted the Life Insurance Policy Illustration Model Regulation, and this is now in effect in most states. The regulation prohibits companies from showing illustrated values that fail a lapse support test, but that test provides a generous safe harbor and does not eliminate undisclosed lapse risk. There is also work in progress on revising the Standard Nonforfeiture Law, and that project will affect future pricing practices. Regulators and industry and consumer groups are debating how to allow innovative products while protecting consumers.

In today’s marketplace, lapse-supported pricing remains a powerful tool that companies can use to create the appearance of low cost, thereby gaining a marketing advantage over competitors whose products actually provide better consumer value.

Advocates of lapse-supported pricing can find their best case in Canada, where valuation and nonforfeiture laws allow product designs that are not possible in the U.S. The Canadian market offers level premium term to age 100 with no cash values, and universal and variable universal life with level cost-of-insurance rates. The term premiums and cost-of-insurance rates are guaranteed, so in Canada it is the insurance companies, not the policyholders, who bear the lapse risk. Of course, all of the policyholders still bear the risk that the company’s solvency will be in jeopardy if too many people decide to keep their policies in force.

How to make lapse-supported pricing work for you

Lapse-supported pricing really can work, and you can use it to get cheap insurance. The trick to making it work for you is to take an activist role. Here are the steps:

Before you buy the policy

  1. Ask the company what lapse rates it is assuming in its pricing. Most companies are happy to disclose their pricing assumptions, because they want people to make informed purchase decisions.Ha ha, just kidding.
  2. Ask the company for a list of people who have already bought the policy that you’re thinking of buying. Choose a random sample and call them. If they seem clueless about what they’ve bought, that’s a good sign. If they seem financially insecure and possibly unable to pay premiums in the future, that’s good, too.

After you buy the policy

  1. Ask the company each year for an update on how many people have actually dropped their policies, and compare that with the original estimate. This will tell you if you need to spring into action (see Steps 4 and 5).
  2. After a few years have passed, give the policyholder list to successful insurance agents that you know. Insurance salespeople are very good at replacing existing policies, because they get a new commission when they do. You can have the best policy that has ever been created in the history of civilization, and there will be at least one agent in your neighborhood who will be able to replace it.
  3. After a few more years have passed, call as many of your fellow policyholders as possible and try to convince them to drop their policies. You can tell them about hot new products in the marketplace, and you can spread false rumors about the company’s financial health and denial of claims.

Remember: Your goal is to exploit the ignorance, overconfidence and misfortune of your fellow policyholders for your benefit. After all, exploitation is what lapse-supported pricing is all about.

For more information

  • American Academy of Actuaries, Proposed New Standard Nonforfeiture Law for Life Insurance (in NAIC Proceedings, 1996 1st Quarter, pp. 861-883).
  • Belth, Joseph M., "Secondary Guarantees, Marketers, Actuaries, Regulators, and a Potential Financial Disaster for the Life Insurance Business," The Insurance Forum, March/April 2004.
  • Belsky, Gary and Thomas Gilovich, Why Smart People Make Big Money Mistakes — and How to Correct Them, Simon & Schuster, 1999 (see Chapter 6, on overconfidence).
  • Buley, R. Carlyle, The American Life Convention, Appleton-Century-Crofts, 1953.
  • Canadian Institute of Actuaries, Valuation Technique Paper #1 — Valuation of Lapse Supported Products, 1985.
  • Cooper, Robert W., An Historical Analysis of the Tontine Principle, Huebner Foundation Monograph No. 1, University of Pennsylvania, 1972.
  • Davis, Ann, "Unexpected Rate Rises Jolt Elders Insured For Long-Term Care, " The Wall Street Journal, June 22, 2000.
  • Jennings, Robert M. and Andrew P. Trout, The Tontine: From the Reign of Louis XIV to the French Revolutionary Era, Huebner Foundation Monograph No. 12, University of Pennsylvania, 1982.
  • Katt, Peter, "Life Insurance Alerts, Tips and Information," January 2000.
  • Katt, Peter, "Permanent Life: Clearing the Fog That Surrounds Policy Cash Values," AAII Journal, November 1994.
  • Kimball, Spencer L. and Jon S. Hanson, "The Regulation of Specialty Policies in Life Insurance," Michigan Law Review, December 1963.
  • Koenig, William C. and Stephen H. Frankel, "Don’t Forfeit Nonforfeiture," Best’s Review, June 2000.
  • Lombardi, Mike, "Another Look at Lapse Supported Products," Marketing Options, April 1996.
  • National Association of Insurance Commissioners, "Determination of Nonforfeiture Benefits and Guaranteed and Non-Guaranteed Elements for Life Insurance and Annuity Contracts Model Act," 11/22/99 draft.
  • Society of Actuaries, "Current Issues in Product Pricing," Record of the Society of Actuaries, Vol. 24, No. 3 (October 1998).
  • Society of Actuaries, "Nonforfeiture Law Developments," Record of the Society of Actuaries, Vol. 22, No. 3 (October 1996).
  • Society of Actuaries, Report of the Society of Actuaries Task Force on Life Nonforfeiture, March 15, 1996 (in NAIC Proceedings, 1996 1st Quarter, pp. 883-897).
  • Society of Actuaries, "Disclosure Systems: Can an Ideal Method Be Found?," Record of the Society of Actuaries, Vol. 17, No. 2 (May 1991).
  • Stalson, J. Owen, Marketing Life Insurance, Harvard University Press, 1942.