An interesting application of Taylor Series can be found in the paper
A.Frey, V.Schmidt.
"Taylor-series expansion for multivariate characteristics of classical risk
processes."
Insurance: Mathematics and Economics, 18(1996), 1-12.
The paper is devoted to the calculation of the joint distribution of ruin
time T and surplus X and deficit Y at ruin time, that is the probability
F(t,x,y)=P{T<t,X<x,Y<y}.
Hope this helps,
Arcady.
=============================================
Arcady A. Novosyolov, Ph.D.
19-149, Academgorodok, Krasnoyarsk, Russia, 660036,
tel. +7 3912 495382 (business), +7 3912 498596 (home)
fax +7 3912 439830 (Mark fax "To A.Novosyolov")
http://www.geocities.com/CapeCanaveral/Launchpad/6016/
-----Original Message-----
From: Christopher Diamantoukos <chrisd@voicenet.com>
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
>
>
>
>Visit the CAS Web Site at http://www.casact.org
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