Contents

• For users of Monte Carlo
  • Introduction
    • Monte Carlo in Finance
    • Option Pricing
    • Interest Rate Models
    • Insurance Applications
    • Monte Carlo
    • Quasi-Random Monte Carlo
  • Discrepancy
    • Variation of a Function
  • Discrepancies
    • One simulation method is as good as another?
    • Simulation methods are black boxes?
    • Error bound of Monte Carlo is ?
    • Discrepancy has no relation to Monte Carlo?
    • Low discrepancy just another tool?
    • Better error bounds than low discrepancy can be invented?
    • Better methods than low discrepancy can be invented?
    • With Simulation Any Method Goes?
    • We don't compute integrals?
  • Cajun Wisdom
    • Its the Discrepancy
    • Part of Integration Theory
    • Its all integration
    • CTE for segregated fund guarantees is a good application
    • Discrepancy measures an integration method
    • QRMC-LDS provides value even for small sets of points
    • Variation on puts
    • Set up with Bounded Variation
    • Its the Theorems
    • Experience is good in many cases
  
  
• Theorems
  • Discrepancy
  • Variation
    • One Dimension
    • Theorems on Variation
    • Hardy Krause variation n-dimensions
  • Monte Carlo Expected Error
  • Koksma's Inequality
  • Koksma-Hlawka's Inequality
  • Niederreiter Theorem 2.12
  • European Put
    • Variation
    • Koksma Inequality
  
  
• Some URLs
  • Boyle
  • Brender
  • Broadie
  • Brown
  • Carothers
  • Craighead
  • Embrechts
  • Hakansson
  • Hancock
  • Hardy
  • Manistre
  • Niederreiter
  • Panjer
  • Papageorgiou
  • Elias Shiu
  • Ken Seng Tan
  • Tenney
  • Traub
  
  
• Bibliography
• Index