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

42 Pages Posted: 5 Jun 2017

See all articles by Pierre Del Moral

Pierre Del Moral

INRIA Bordeaux-Sud Ouest; University of Bordeaux - University of Bordeaux 1

Gareth Peters

Department of Actuarial Mathematics and Statistics, Heriot-Watt University; University College London - Department of Statistical Science; University of Oxford - Oxford-Man Institute of Quantitative Finance; London School of Economics & Political Science (LSE) - Systemic Risk Centre; University of New South Wales (UNSW) - Faculty of Science

Christelle Verge

Independent

Date Written: 2012

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 compliment alternative approaches adopted in risk management, including closed from 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 in a principled fashion the general framework of interacting particle methods, which goes well beyond the standard particle filtering framework and Sequential Monte Carlo frameworks to instead 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 which we reinterpret under a Feynman-Kac particle integration framework. These functional models are natural mathematical extensions of the traditional change of probability measures, common in designing importance samplers. Practically, the particles evolve randomly around the space independently and to each particle is associated a positive potential function. Periodically, particles with high potentials duplicate at the expense of low potential particle which die. This natural genetic type selection scheme appears in numerous applications in applied probability, physics, Bayesian statistics, signal processing, biology, and information engineering. It is the intention of this paper to introduce them to risk modeling.

Keywords: insurance, particle filtering, sequential monte carlo, accept-reject, Feynmann-Kac Interacting Particles

Suggested Citation

Del Moral, Pierre and Peters, Gareth and Verge, Christelle, An Introduction to Stochastic Particle Integration Methods: With Applications to Risk and Insurance (2012). Available at SSRN: https://ssrn.com/abstract=2980466 or http://dx.doi.org/10.2139/ssrn.2980466

Pierre Del Moral

INRIA Bordeaux-Sud Ouest ( email )

351, cours de la Liberation
Bordeaux, 33405
France
+33 05 40 00 21 13 (Phone)

HOME PAGE: http://www.math.u-bordeaux1.fr/~delmoral/

University of Bordeaux - University of Bordeaux 1

351 cours de la Libération
33405 TALENCE cedex
France

Gareth Peters (Contact Author)

Department of Actuarial Mathematics and Statistics, Heriot-Watt University ( email )

Edinburgh Campus
Edinburgh, EH14 4AS
United Kingdom

HOME PAGE: http://garethpeters78.wixsite.com/garethwpeters

University College London - Department of Statistical Science ( email )

1-19 Torrington Place
London, WC1 7HB
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

University of Oxford Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

London School of Economics & Political Science (LSE) - Systemic Risk Centre ( email )

Houghton St
London
United Kingdom

University of New South Wales (UNSW) - Faculty of Science ( email )

Australia

Christelle Verge

Independent

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