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14 - Basic Monte Carlo methods

from Part IV - Model construction and evaluation

Published online by Cambridge University Press:  05 June 2012

Yiu-Kuen Tse
Affiliation:
Singapore Management University
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Summary

Some problems arising from loss modeling may be analytically intractable. Many of these problems, however, can be formulated in a stochastic framework, with a solution that can be estimated empirically. This approach is called Monte Carlo simulation. It involves drawing samples of observations randomly according to the distribution required, in a manner determined by the analytic problem.

To solve the stochastic problem, samples of the specified distribution have to be generated, invariably using computational algorithms. The basic random number generators required in Monte Carlo methods are for generating observations from the uniform distribution. Building upon uniform random number generators, we can generate observations from other distributions by constructing appropriate random number generators, using methods such as inverse transformation and acceptance–rejection. We survey specific random number generators for some commonly used distributions, some of which are substantially more efficient than standard methods. An alternative method of generating numbers resembling a uniformly distributed sample of observations is the quasi-random number generator or the low-discrepancy sequence.

The accuracy of the Monte Carlo estimates depends on the variance of the estimator. To speed up the convergence of the Monte Carlo estimator to the deterministic solution, we consider designs of Monte Carlo sampling schemes and estimation methods that will produce smaller variances. Methods involving the use of antithetic variable, control variable, and importance sampling are discussed.

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Chapter
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Nonlife Actuarial Models
Theory, Methods and Evaluation
, pp. 400 - 434
Publisher: Cambridge University Press
Print publication year: 2009

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  • Basic Monte Carlo methods
  • Yiu-Kuen Tse, Singapore Management University
  • Book: Nonlife Actuarial Models
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511812156.020
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  • Basic Monte Carlo methods
  • Yiu-Kuen Tse, Singapore Management University
  • Book: Nonlife Actuarial Models
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511812156.020
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Basic Monte Carlo methods
  • Yiu-Kuen Tse, Singapore Management University
  • Book: Nonlife Actuarial Models
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511812156.020
Available formats
×