View Full Version : Pure prem exponential trend

piemedia

02-01-2012, 04:47 PM

Dear friends, please show me how to calculate the exponential trend factor for Pure prem. In "Basic ratemaking", page 352 (A-15):

yr ending Q - X Pure prem

2014-4 60.03

2015-1 60.49

2015-2 60.86

2015-3 61.37

2015-4 61.28

then; pure premium exponential trend at 4 pt is 1.9%. How do you get the 1.9%?

Many thank you!!

Vorian Atreides

02-01-2012, 05:32 PM

Place the last 4 points in your TI-30X 2-variable statistic analysis, but use ln(y) instead of y.

The slope of this regression (I get a = 0.004727136) is the quarterly trend.

So, (1 + a)^4 - 1 = 0.0190 or 1.9%.

(Alternately, you could use the regression formula to calculate the model results at 2015-4 and 2016-4--I get 61.43 and 62.61, respectively--and calculate the trend from these two points.)

piemedia

02-01-2012, 06:38 PM

Place the last 4 points in your TI-30X 2-variable statistic analysis, but use ln(y) instead of y.

The slope of this regression (I get a = 0.004727136) is the quarterly trend.

So, (1 + a)^4 - 1 = 0.0190 or 1.9%.

(Alternately, you could use the regression formula to calculate the model results at 2015-4 and 2016-4--I get 61.43 and 62.61, respectively--and calculate the trend from these two points.)

Sorry to ask!! How did you get the a=0.004727136? Thank you very much in advance.

piemedia

02-01-2012, 07:25 PM

Sorry to ask!! How did you get the a=0.004727136? Thank you very much in advance.

Did you use a= (E(xy)-E(x)E(y) )/( E(x^2)-E(x)^2 ) ?

http://www.actuarialoutpost.com/actuarial_discussion_forum/showpost.php?p=5003501&postcount=2

What's funny about my link is two things:

- Vorian answered almost the same question before

- It's almost exactly the one-year anniversary of that post.

Vorian Atreides

02-02-2012, 12:10 AM

:lol: I forgot about that post.

Vorian Atreides

02-02-2012, 12:12 AM

Did you use a= (E(xy)-E(x)E(y) )/( E(x^2)-E(x)^2 ) ?

I pushed 2nd STAT, selected two-variable.

Pushed Data, entered 1 for x1, ln(60.49) for y1; proceed in a similar manner for the next three data points.

Press STATVAR. Press the left arrow until the value for a appears.

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