Showing posts sorted by relevance for query langton. Sort by date Show all posts
Showing posts sorted by relevance for query langton. Sort by date Show all posts

Dec 12, 2011

Forecast Period Principle

As actuaries we mostly try to shape the data for our models (ALM, Stress Tests, Assessments, Etc.)  on basis of economic scenarios.

Recently we have experienced (Sub prime crisis, Bank crisis, Country crisis, Currency crisis, Debt crisis, etc) that our economy isn't that stable as we might perhaps have estimated or hoped (what's the difference nowadays?) .............

In other words:

Our Economy is chaotic by nature

Therefore, to learn how to shape our data, models and equations in a more chaotic or fuzzy way, let's take a look at the more chaotic processes of nature self.

Sea Level Rising
As an example let's pick out a major discussion: Sea level rising!
The discussion around this topic resembles the fuzzy way we discuss our economic and financial system. Some say sea level is rising and our (grand)children will surely drown. Others tell us not to worry. Who's right?

As the above graph - based on data of the University of Colorado - clearly shows, sea level is rising (Trend: ~3.1mm/year).

But just like in risk management models, the devil is in the details and (on the other hand) God's wisdom rules in time......

Actuarial devil watchers will have noticed a strange 'hockey schtick' in the above graph: Sea level is actually declining since 2007. 

This leads to the key question: 

What is a reliable Sea Level long term forecast?

How to answer this question...

Forecast Period Principle
To draw sensible forecast conclusions, the period of the measured and analyzed historical facts and their (explaining) context, has to be of  the same order of magnitude as the period we use to (context-dependable) project our data in the future.

So if we want to say something about for instance the next 14000 years, we should (also) look back 14000 years:

From the above chart it's clear that forecasts about sea level forecast on basis of 4, 10 or even  50 years are madman's exercises and useless.

On the long term (10-100 years) sea level will most likely keep rising at an average 3-4mm/year rate. So you don't need to calculate if your home will turn into an houseboat, unless....

Pension Funds and 'Forecast Period Principle'
Now let's apply the 'Forecast Period Principle' on pension funds...
  • Pension funds have a life span of more than hundred years, pension fund members have a life span of about 70-80 years.
  • Therefore projections and valuation of pension funds should also take place on basis of periods and (long) term discount rates of the same order of magnitude (10-50-100 years) as their life span. 
  • This implies that calculating coverage ratio's on a daily basis is perhaps a nice way to make a living as actuary, but practical completely inadequate. As it serves no goal, leads to unnecessary worries  and misleads pension board members. 
  • Lesson: calculate coverage ratios on 1,5 and 10 year basis and take action if all these coverage ratios start pointing in the same direction....

Unless.... : Langton Warning Principle

Yet, if you calculated your forecast on basis of the 'Forecast Period Principle', do not go to sleep peacefully!

Even if your models and visual inspection indicate a steady development, there's always the risk of a sudden 'Langton's Event' (loss).

In other words:

  1. Sea levels could suddenly Rise..
  2. Study Suddenly Rise Scenarios to prevent false alarm

    So take the 'Langton Warning Principle' serious and try to stay alert as risk manager in every possible circumstance.

    Do you want to learn more about Langton's principle? Read: Langton's Actuarial Ant

    'Crisis' will become business as usual for actuaries. Coming years, our short term 'Langton Warning Principle models' will be just as important as our steady forecasts on basis of  the 'Forecast Period Principle'. Don't mix them up!!

    Keep in mind the warning of NOAA Administrator Jane Lubchenco:

    We have good reason to believe that what happened this year is not an anomaly, but instead is a harbinger of what is to come.
                                      NOAA Administrator Jane Lubchenco (2011)

    Key Question
    Finally, the crisis key question will be:
    Are we Sinking or Thinking?

    Answer: It's all a matter of communication!

    Related links/Sources
    - Langton's Actuarial Ant
    - Colorado University: Sea level 
    - Some Actuarial Formula of Life Insurance for Fuzzy Markets
    - Google books: Actuaries' survival guide: how to succeed
    - Fractals & Actuaries (1997)
    - What about my town, when sea level rises X meter?
    - actual and historical sea levels: sea levels online
    - Sea levels Online
    - NOAA Report
    - Sea level Spredsheet of this Blog 
    - Original Picture: Climate Change Science Compendium 2009

    Feb 22, 2009

    Langton's Actuarial Ant

    As an actuary, you believe in the consistency of your risk models.

    You might think that with 10.000 observations you've got enough stuff to present a consistent statistical model with realistic expectations, variances, etc.

    You are aware that the output of your model depends on the quality of the data and the assumptions. In your advice you try to communicate all that to the board in order to support sound and responsible decisions.

    In other words, you've got a consistent model and, as an actuary with a professional and consistent life-philosophy, you have everything under control. No great changes will take place?


    you're probably wrong !

    Just like our models, we actuaries, are not consistent

    Even if we (or the risk reality we try to model) act in a stable consistent way, we (or risk reality) keep interfering with our environment and our environment responses to us.

    At first this response seems meaningless and of no value. You think you're consequent and your work and achievements in life seem relatively stable, perhaps a little bit chaotic and of no great significance. But in repeating your proven receipts, way of doing or procedures endlessly, eventually

    Something will change

    This change often will not appear as an evolution in your life, but as a kind of revolution, out of the blue and most often unexpected.
    Suddenly, just like in the credit crisis, there's an emerging situation. The way you always did it, doesn't turn out right anymore. Your model crashed, you crashed and there was nothing you could do about it. You couldn't have foreseen it, you could not have prevented it the classical way.

    That's why we always have to add some non-classical extra 'common sense' safety margin thinking in our models.

    The other side of this is also true. Fore example, when you study, you'll probably, once in a while, think: what progress am I making?

    But don't worry, if you keep on your track, there'll be a day your future suddenly comes to you (out of the blue: as a kind of emergent property) instead of "the you trying to make your future" in this Game of Life.

    A good demonstration of this principle is

    Langton's ant

    Langton's ant is an virtual ant that starts out on a grid containing black and white cells, and then follows the following set of rules.

    1. If the ant is on a black square, it turns right 90° and moves forward one unit.
    2. If the ant is on a white square, it turns left 90° and moves forward one unit.
    3. When the ant leaves a square, it inverts the color.

    The result is a quite complicated and apparently chaotic, but relatively stable, motion. But after about 10.000 moves the ant starts to build a broad diagonal "highway".

    So keep in mind "Langton's Actuarial Ant" next time you design a new risk model.

    Anyhow, stay on your track as an actuary and remember, whether it's you in life or your models, someday there'll be

    a collapse of chaos