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An Introduction to Stochastic Particle Integration Methods: With Applications to Risk and Insurance

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Monte Carlo and Quasi-Monte Carlo Methods 2012

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 65))

Abstract

This article presents a guided introduction to a general class of interacting particle methods and explains throughout how such methods may be adapted to solve general classes of inference problems encountered in actuarial science and risk management. Along the way, the resulting specialized Monte Carlo solutions are discussed in the context of how they complemented alternative approaches adopted in risk management, including closed form bounds and asymptotic results for functionals of tails of risk processes.

The development of the article starts from the premise that whilst interacting particle methods are increasingly used to sample from complex and high-dimensional distributions, they have yet to be generally adopted in inferential problems in risk and insurance. Therefore, we introduce a range of methods which can all be interpreted in the general framework of interacting particle methods, which goes well beyond the standard particle filtering framework and Sequential Monte Carlo frameworks. For the applications we consider in risk and insurance we focus on particular classes of interacting particle genetic type algorithms. These stochastic particle integration techniques can be interpreted as a universal acceptance-rejection sequential particle sampler equipped with adaptive and interacting recycling mechanisms. We detail how one may reinterpret these stochastic particle integration techniques under a Feynman-Kac particle integration framework. In the process, we illustrate how such frameworks act as natural mathematical extensions of the traditional change of probability measures, common in designing importance samplers for risk managements applications.

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Author notes

  1. Gareth W. Peters

    Present address: Department of Statistical Science, University College London, London, UK

Authors and Affiliations

  1. INRIA Bordeaux-Sud Ouest, and Bordeaux Mathematical Institute, Ecole Polytechnique (CMAP), Palaiseau, Paris, France

    Pierre Del Moral

  2. School of Mathematics and Statistics, University of New South Wales, Sydney, NSW, Australia

    Gareth W. Peters

  3. CMIS – Commonwealth Scientific and Industrial Research Organization, Sydney, Australia

    Gareth W. Peters

  4. ONERA – The French Aerospace Lab, F-91761, Palaiseau, Paris, France

    Christelle Vergé

Authors
  1. Pierre Del Moral
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  2. Gareth W. Peters
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  3. Christelle Vergé
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Corresponding author

Correspondence to Pierre Del Moral .

Editor information

Editors and Affiliations

  1. The University of New South Wales School of Mathematics and Statistics, Sydney, New South Wales, Australia

    Josef Dick

  2. The University of New South Wales School of Mathematics and Statistics, Sydney, New South Wales, Australia

    Frances Y. Kuo

  3. The University of New South Wales School of Mathematics and Statistics, Sydney, New South Wales, Australia

    Gareth W. Peters

  4. The University of New South Wales School of Mathematics and Statistics, Sydney, New South Wales, Australia

    Ian H. Sloan

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Del Moral, P., Peters, G.W., Vergé, C. (2013). An Introduction to Stochastic Particle Integration Methods: With Applications to Risk and Insurance. In: Dick, J., Kuo, F., Peters, G., Sloan, I. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2012. Springer Proceedings in Mathematics & Statistics, vol 65. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41095-6_3

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