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 2 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 3 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 4 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  … 5 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? 6 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 7 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  8 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 9 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 33 and the variance is 1 2 2 2 s  ((1)  0 1 )  1 2 <Excel – variance demo> 10 Numerical Excellence in Finance