Once upon a time...

Imagine there were ten insurance sectors, each sector being a different large risk (or possibly the same risks, in different geographical areas). All of these risks are taken to be independent.

To simplify, we assume that all the risks follow the same yearly payout distributions. The details of the distribution doesn't matter much for the argument, but in this toy model, the payouts follow the discrete binomial distribution with n=10 and p=0.5, with millions of pounds as the unit:

This means that the probability that each sector pays out £n million each year is (0.5)^{10 .} 10!/(n!(10-n)!).

All these companies are bound by Solvency II-like requirements, that mandate that they have to be 99.5% sure to payout all their policies in a given year - or, put another way, that they only fail to payout once in every 200 years on average. To do so, in each sector, the insurance companies have to have capital totalling £9 million available every year (the red dashed line).

Assume that each sector expects £1 million in total yearly expected profit. Then since the expected payout is £5 million, each sector will charge £6 million a year in premiums. They must thus maintain a capital reserve of £3 million each year (they get £6 million in premiums, and must maintain a total of £9 million). They thus invest £3 million to get an expected profit of £1 million - a tidy profit!

Every two hundred years, one of the insurance sectors goes bust and has to be bailed out somehow; every hundred billion trillion years, all ten insurance sectors go bust all at the same time. We assume this is too big to be bailed out, and there's a grand collapse of the whole insurance industry with knock on effects throughout the economy.

But now assume that insurance companies are allowed to invest in each other's sectors. The most efficient way of doing so is to buy equally in each of the ten sectors. The payouts across the market as a whole are now described by the discrete binomial distribution with n=100 and p=0.5:

This is a much narrower distribution (relative to its mean). In order to have enough capital to payout 99.5% of the time, the whole industry needs only keep £63 million in capital (the red dashed line). Note that this is far less that the combined capital for each sector when they were separate, which would be ten times £9 million, or £90 million (the pink dashed line). There is thus a profit taking opportunity in this area (it comes from the fact that the standard deviation of X+Y is less that the standard deviation of X plus the standard deviation Y).

If the industry still expects to make an expected profit of £1 million per sector, this comes to £10 million total. The expected payout is £50 million, so they will charge £60 million in premium. To accomplish their Solvency II obligations, they still need to hold an extra £3 million in capital (since £63 million - £60 million = £3 million). However, this is now across the whole insurance industry, not just per sector.

Thus they expect profits of £10 million based on holding capital of £3 million - astronomical profits! Of course, that assumes that the insurance companies capture all the surplus from cross investing; in reality there would be competition, and a buyer surplus as well. But the general point is that there is a vast profit opportunity available from cross-investing, and thus if these investments are possible, they will be made. This conclusion is not dependent on the specific assumptions of the model, but captures the general result that insuring independent risks reduces total risk.

But note what has happened now: once every 200 years, an insurance company that has spread their investments across the ten sectors will be unable to payout what they owe. However, every company will be following this strategy! So when one goes bust, they all go bust. Thus the complete collapse of the insurance industry is no longer a one in hundred billion trillion year event, but a one in two hundred year event. The risk for each company has stayed the same (and their profits have gone up), but the systemic risk across the whole insurance industry has gone up tremendously.

...and they failed to live happily ever after for very much longer.

My uncle works in insurance. I recently mentioned that I'm planning to sign up for cryonics.

"That's amazing," he said. "Convincing a young person to buy life insurance? That has to be the greatest scam ever."

I took the comment lightly, not caring to argue about it. But it got me thinking - couldn't cryonics be a great opportunity for insurance companies to make a bunch of money?

Consider:

1. Were there a much stronger demand for cryonics, cryonics organizations would flourish through competition, outside investment, and internal reinvestment. Costs would likely fall, and this would be good for cryonicists in general.
2. If cryonics organizations flourish, this increases the probability of cryonics working. I can think of a bunch of ways in which this could happen; perhaps, for example, it would encourage the creation of safety nets whereby the failure of individual companies doesn't result in anyone getting thawed. It would increase R&D on both perfusion and revivification, encourage entrepreneurs to explore new related business models, etcetera.
3. Increasing the demand for cryonics increases the demand for life insurance policies; thus insurance companies have a strong incentive to increase the demand for cryonics. Many large insurance companies would like nothing more than to usher in a generation of young people that want to buy life insurance.¹
   
4. The demand for cryonics could be increased by an insightful marketing campaign by an excellent marketing agency with an enormous budget... like those used by big insurance companies.² A quick Googling says that ad spending by insurance companies exceeded $4.15 billion in 2009.

Almost a year ago, Strange7 suggested that cryonics organizations could run this kind of marketing campaign. I think he's wrong - there's no way CI or Alcor have the money. But the biggest insurance companies do have the money, and I'd be shocked if these companies or their agencies aren't already dumping all kinds of money into market research.

What would doing this require? 

1. That an open-minded person in the insurance industry who is in the position to direct this kind of funding exists. I don't have a sense of how likely this is.
2. That we can locate/get an audience with the person from step 1. I think research and networking could get this done, especially if the higher-status among us are interested.
3. That we can find someone who is capable and willing to explain this clearly and convincingly to the person from step 1. I'm not sure it would be that difficult. In the startup world, strangers convince strangers to speculatively spend millions of dollars every week. Hell, I'll do it.

I want to live in a world where cryonics ads air on TV just as often as ads for everything else people spend money on. I really can see an insurance company owning this project - if they can a) successfully revamp the image of cryonics and b) become known as the household name for it when the market gets big, they will make lots of money.

What do you think? Where has my reasoning failed? Does anyone here know anyone powerful in insurance? 

Lastly, taking a cue from ciphergoth: this is not the place to rehash all the old arguments about cryonics. I'm asking about a very specific idea about marketing and life insurance, not requesting commentary on cryonics itself. Thanks!

¹ Perhaps modeling the potential size of the market would offer insight here. If it turns out that this idea is not insane, I'll find a way to make it happen. I could use your help.

² Consider what happened with diamonds in the 1900s:

... N. W. Ayer suggested that through a well-orchestrated advertising and public-relations campaign it could have a significant impact on the "social attitudes of the public at large and thereby channel American spending toward larger and more expensive diamonds instead of "competitive luxuries." Specifically, the Ayer study stressed the need to strengthen the association in the public's mind of diamonds with romance. Since "young men buy over 90% of all engagement rings" it would be crucial to inculcate in them the idea that diamonds were a gift of love: the larger and finer the diamond, the greater the expression of love. Similarly, young women had to be encouraged to view diamonds as an integral part of any romantic courtship.

Let's say we (as a country) ban life insurance and health insurance as separate packages [1] and require them to be combined in something I'll call "Longevity Insurance".  The idea is that as a person/consumer, you can buy a "life expectancy" of 75 years, or 90 years, or whatever. In addition, you specify a maximum dollar amount that the longevity insurance will ever pay out--say, $2 million. If you have any medical issues throughout your life, up to the life expectancy threshold, the insurance plan will pay for your expenses. If it fails to keep you consciously alive for the duration of your "life expectancy", then upon your death, the policy guarantees that the company will pay the full remaining amount to your next of kin.

It seems like this arrangement would put all of the right incentives [2] in place for both companies and individuals. Most individuals would want to avoid trivial medical expenses in order to maximize payout to family in case of accidental death. Companies would want to maximize health and longevity in order to profit from the end-of-life payout. And our society would have a way to rationally consider the value of life without resorting to arguments that essentially conclude "life is of infinite value," and in doing so, prevent sensible gerontological triage. To put it into perspective, it makes little sense that we spend $1M (as a society) trying to save a 92-year-old when that same amount could have saved 10 teenagers.

Longevity Insurance companies would be incentivized to become heavily involved in medical research that prevents disease, prolongs life, and keeps people healthy. I can imagine a whole array of things that make sense in this context. For example, it would be the right place to fund studies on genetics, it could be the right vehicle for getting 'free' immunizations, and it could even make public funding for "health insurance" easier to pass--simply set the bar low enough that everyone can agree on an age that society will extend a policy for. Do we all agree that everyone in our society should live to age 50? Super! The government will cover Longevity Insurance up to age 50.

[1] We could also just allow Longevity Insurance as a free-market alternative, but for the sake of argument, let's ban its competitors.

[2] The one incentive that Longevity Insurance does not seem to address well is the possibility of next-of-kin killing their loved one just prior to the end of an insurance policy. One option would be to require a one-year moratorium in the case where someone dies within a year of their policy ending. This would give time for an investigation before awarding large sums of money.

* crosspost from my blog, http://halfcupofsugar.com/longevity-insurance

I was offered life insurance and thought I need input from LessWrong people before I accept or decline the offer.

Please share your personal experience, if any, with me.

Thoughts that have occurred to me:

What are the odds that that company will be around in 38 years? I mean, both World Wars fit in that time span.

What is the probability distribution over how much the Euro will have inflated by then? Does that even matter?