RE: Taylor Series in Actuarial Science.

Sce, Michael ( (no email) )
Tue, 30 Mar 1999 08:08:40 -0500

I've read some very interesting replies where Taylor series was used, and I
am impressed. This has contradicted what I previously thought, which was
that the Taylor series has gone the way of the dinosaur. Further, we have
substituted stochastic processes, for the deterministic. Taylor series
falls into the latter category. Other methodologies, such as simulation,
have taken over in many areas of actuarial science. The advent of the
desktop computer has changed all (or much of) that.

But some suggestions where the Taylor series is used seems to me to not
really be the series, but funky algebraic substitutes that could look like
one. For example, the age-to-age, age-to-ultimate loss development factors.
Is that really deserving of the name?

Ok, guys, fire away!

Michael

-----Original Message-----
From: Christopher Diamantoukos [SMTP:chrisd@voicenet.com]
Sent: Thursday, March 18, 1999 7:24 PM
To: Rob Coridan; CASNET
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Subject: Taylor Series in Actuarial Science.

I don't know how I recieved this letter, but perhaps this can get to
the
CAS list.

In reply, there are two conceptual applications that I have
encountered
Taylor Series in actuarial science applications:

1. The convergence of a development or extrapolation parameter,
such as
the estimated mean age-to-ultimate "loss" development factor.

2, The approximation of statistical parameters to a desired degree
of
"significance", such as the first or second order approximation of
the
variance of an analytical random variable form. An example of such
a
form might be a simple form of x/y, where interest is in the random
variable z that is equal to this analytical random variable form,
i.e.
z=x/y.

I hope this stimulates some discussion.

Christopher Diamantoukos, FCAS

Rob Coridan wrote:

> Hello, I'm sorry to bother you, but my name is Robert Coridan
and
> I am a student in the Actuarial Science at the Ohio State
University.
> We've been learning several techniques for approximation in my
> calculus class, and I was wondering....as actuaries, can you think
of
> an example of an instance where you would ever use the Taylor
Series?
> Any suggestions you can give me, no matter how brief, would be
greatly
> appreciated. Thank you! -Robert

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