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Title: Fast Fourier Transform for multivariate aggregate claims

Abstract

The Fast Fourier Transform provides an alternative approximate method to evaluate the distribution of aggregate losses in insurance and finance. The efficiency of this method has already been proved for univariate and bivariate insurance models; therefore, in this paper, we extend it to a multivariate setting by considering its application to a particular model that includes losses of different types and dependency between them. Since the Fourier transform method works with truncated claims distributions, it can generate aliasing errors by wrapping around the probability mass that lies at the truncation point below this point. To eliminate this problem, we also discuss a suitable change of measure called exponential tilting that forces the tail of the distribution to decrease at exponential rate. Other possible errors are also discussed. We also illustrate the method on several numerical examples.

Authors:
 [1];  [2]
  1. University of Bucharest, Faculty of Mathematics and Computer Science (Romania)
  2. Ovidius University of Constanta, Faculty of Mathematics and Computer Science (Romania)
Publication Date:
OSTI Identifier:
22769392
Resource Type:
Journal Article
Journal Name:
Computational and Applied Mathematics
Additional Journal Information:
Journal Volume: 37; Journal Issue: 1; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; APPROXIMATIONS; FOURIER TRANSFORMATION; MULTIVARIATE ANALYSIS

Citation Formats

Robe-Voinea, Elena-Gratiela, and Vernic, Raluca. Fast Fourier Transform for multivariate aggregate claims. United States: N. p., 2018. Web. doi:10.1007/S40314-016-0336-6.
Robe-Voinea, Elena-Gratiela, & Vernic, Raluca. Fast Fourier Transform for multivariate aggregate claims. United States. doi:10.1007/S40314-016-0336-6.
Robe-Voinea, Elena-Gratiela, and Vernic, Raluca. Thu . "Fast Fourier Transform for multivariate aggregate claims". United States. doi:10.1007/S40314-016-0336-6.
@article{osti_22769392,
title = {Fast Fourier Transform for multivariate aggregate claims},
author = {Robe-Voinea, Elena-Gratiela and Vernic, Raluca},
abstractNote = {The Fast Fourier Transform provides an alternative approximate method to evaluate the distribution of aggregate losses in insurance and finance. The efficiency of this method has already been proved for univariate and bivariate insurance models; therefore, in this paper, we extend it to a multivariate setting by considering its application to a particular model that includes losses of different types and dependency between them. Since the Fourier transform method works with truncated claims distributions, it can generate aliasing errors by wrapping around the probability mass that lies at the truncation point below this point. To eliminate this problem, we also discuss a suitable change of measure called exponential tilting that forces the tail of the distribution to decrease at exponential rate. Other possible errors are also discussed. We also illustrate the method on several numerical examples.},
doi = {10.1007/S40314-016-0336-6},
journal = {Computational and Applied Mathematics},
issn = {0101-8205},
number = 1,
volume = 37,
place = {United States},
year = {2018},
month = {3}
}