Numerical software & tools for the actuarial community

63 Pages·2012·1.96 MB·English

by  Ian Reid

Numerical software & tools
for the actuarial community
John Holden
Jacques du Toit

11th September 2012

Actuarial Teachers' and Researchers'
Conference
University of Leicester

Experts in numerical algorithms
and HPC services
Agenda

NAG Introduction

Software providers to the Insurance Market

Numerical computation – why bother
Problems in numerical computation

NAG’s Numerical Libraries and Toolboxes


Computational problems in Actuarial Science
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Numerical Excellence in Finance
Numerical Algorithms Group - What We Do

NAG provides mathematical and statistical algorithm
libraries widely used in industry and academia

Established in 1970 with offices in Oxford, Manchester,
Chicago, Taipei, Tokyo

Not-for-profit organisation committed to research &
development

Library code written and contributed by some of the
world’s most renowned mathematicians and computer
scientists

NAG’s numerical code is embedded within many vendor
libraries such as AMD and Intel

Many collaborative projects – e.g. CSE Support to the UK’s
largest supercomputer, HECToR
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Numerical Excellence in Finance
Portfolio

Numerical Libraries
Highly flexible for use in many computing languages, programming

environments, hardware platforms and for high performance
computing methods
 Connector Products for Excel, MATLAB, .NET, R and Java
Giving users of the spreadsheets and mathematical software packages

access to NAG’s library of highly optimized and often superior
numerical routines
 NAG Fortran Compiler and GUI based Windows
Compiler: Fortran Builder
 Visualization and graphics software
Build data visualization applications with NAG’s IRIS Explorer

 Consultancy services
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Numerical Excellence in Finance
Software providers to the Insurance Market
 ..
 ACTUARIS
 ..
 AIR Worldwide
 Microsoft
 Algorithmics
 The Numerical Algorithms Group
 Aon Benfield
(NAG)
 ARC
 Oracle Financial Services
 AXIS
 PolySytems
 Barrie & Hibbert
 RMS
 BPS Resolver
 SAS Institute
 BWise
 SunGard
 ClusterSeven
 Towers Watson
 Conducter
 Trillium Software
 Conning
 Ultimate Risk Solutions
 …
 WySTAR
 …

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Numerical Excellence in Finance
How is this software made?

Do these software providers write all their own
code?


Do these software providers write all their own
Numerical Code?


Why not?

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Numerical Excellence in Finance
How is this software made?

Do these software providers write all their own
code?
No


Do these software providers write all their own
Numerical Code?
No


Why not?
Let’s take a look
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Numerical Excellence in Finance
Why bother?

Numerical computation is difficult to do
accurately

Problems of
Overflow / underflow

How does the computation behave for large / small numbers?

Condition

How is it affected by small changes in the input?

Stability

How sensitive is the computation to rounding errors?


Importance of
error analysis

information about error bounds on solution


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Numerical Excellence in Finance
An example: sample variance

For a collection of observations

{{xx ,, ii  11......nn}}
{x , i  1...n}
ii
i
the mean is defined as

111 nnn

xxx  xxx

iii
nnn

iii111
and the variance as
111 nnn
222  222
sss  (((xxx  xxx)))
iii
nnn 111
iii111
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Numerical Excellence in Finance
Example calculation
 For this collection of observations

{{cc 11,,cc,,cc 11}}

the mean is

11
xx  ((cc 11 cc  cc 11))  cc
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and the variance is
1
2 2 2
s  ((1)  0 1 )  1
2
<Excel – variance demo>
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Numerical Excellence in Finance