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LRMoE.jl: a software package for insurance loss modelling using mixture of experts regression model

Published online by Cambridge University Press:  18 March 2021

Spark C. Tseung ,
Andrei L. Badescu ,
Tsz Chai Fung  and
X. Sheldon Lin
Spark C. Tseung
Affiliation:
Department of Statistical Sciences, University of Toronto, 100 St George Street, Toronto, ONM5S 3G3, Canada
Andrei L. Badescu
Affiliation:
Department of Statistical Sciences, University of Toronto, 100 St George Street, Toronto, ONM5S 3G3, Canada
Tsz Chai Fung
Affiliation:
RiskLab, Department of Mathematics, ETH Zurich, Zurich 8092, Switzerland, Department of Risk Management and Insurance, Georgia State University, Atlanta, GA30303, USA
X. Sheldon Lin*
Affiliation:
Department of Statistical Sciences, University of Toronto, 100 St George Street, Toronto, ONM5S 3G3, Canada
*
*Corresponding author. E-mail: [email protected]
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Abstract

This paper introduces a new julia package, LRMoE, a statistical software tailor-made for actuarial applications, which allows actuarial researchers and practitioners to model and analyse insurance loss frequencies and severities using the Logit-weighted Reduced Mixture-of-Experts (LRMoE) model. LRMoE offers several new distinctive features which are motivated by various actuarial applications and mostly cannot be achieved using existing packages for mixture models. Key features include a wider coverage on frequency and severity distributions and their zero inflation, the flexibility to vary classes of distributions across components, parameter estimation under data censoring and truncation and a collection of insurance ratemaking and reserving functions. The package also provides several model evaluation and visualisation functions to help users easily analyse the performance of the fitted model and interpret the model in insurance contexts.

Keywords

Multivariate regression analysisCensoring and truncationExpectation conditional maximisation algorithmInsurance ratemaking and reservingjulia
Type
Paper
Information
Annals of Actuarial Science , Volume 15 , Issue 2 , July 2021 , pp. 419 - 440
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Institute and Faculty of Actuaries

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References

Blostein, M. & Miljkovic, T. (2019). On modeling left-truncated loss data using mixtures of distributions. Insurance: Mathematics and Economics, 85, 35–46. ISSN 0167-6687.Google Scholar
Dempster, A.P., Laird, N.M. & Rubin, D.B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society: Series B (Methodological), 39(1), 1–22.Google Scholar
Dutang, C. & Charpentier, A. (2019). CASdatasets: insurance datasets. R package version 1.0-10.Google Scholar
Fan, J. & Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association, 96(456), 1348–1360.CrossRefGoogle Scholar
Friedman, J.H. (2001). Greedy function approximation: a gradient boosting machine. Annals of Statistics, 29(5), 1189–1232.CrossRefGoogle Scholar
Fung, T.C., Badescu, A.L. & Lin, X.S. (2019a). A class of mixture of experts models for general insurance: application to correlated claim frequencies. ASTIN Bulletin, 49(3), 647–688.CrossRefGoogle Scholar
Fung, T.C., Badescu, A.L. & Lin, X.S. (2019b). A class of mixture of experts models for general insurance: theoretical developments. Insurance: Mathematics and Economics, 89, 111–127.Google Scholar
Fung, T.C., Badescu, A.L. & Lin, X.S. (2020a). Fitting censored and truncated regression data using the mixture of experts models. Available in SSRN: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3740061CrossRefGoogle Scholar
Fung, T.C., Badescu, A.L. & Lin, X.S. (forthcoming). A new class of severity regression models with an application to IBNR prediction. North American Actuarial Journal. https://doi.org/10.1080/10920277.2020.1729813CrossRefGoogle Scholar
Grün, B. & Leisch, F. (2004). Bootstrapping Finite Mixture Models. Mathematics.Google Scholar
Grün, B. & Leisch, F. (2008). FlexMix version 2: finite mixtures with concomitant variables and varying and constant parameters. Journal of Statistical Software, 28(4), 1–35.CrossRefGoogle Scholar
Gui, W., Huang, R. & Lin, X.S. (2018). Fitting the Erlang mixture model to data via a GEM-CMM algorithm. Journal of Computational and Applied Mathematics, 343, 189–205.CrossRefGoogle Scholar
Jiang, W. & Tanner, M.A. (1999). On the identifiability of mixtures-of-experts. Neural Networks, 12(9), 1253–1258.CrossRefGoogle ScholarPubMed
Jordan, M.I. & Jacobs, R.A. (1994). Hierarchical mixtures of experts and the EM algorithm. Neural Computation, 6(2), 181–214.CrossRefGoogle Scholar
Lee, D., Li, W.K. & Wong, T.S.T. (2012). Modeling insurance claims via a mixture exponential model combined with peaks-over-threshold approach. Insurance: Mathematics and Economics, 51(3), 538–550.Google Scholar
Leisch, F. (2004). FlexMix: a general framework for finite mixture models and latent class regression in R. Journal of Statistical Software, 11(8), 1–18.CrossRefGoogle Scholar
McLachlan, G. & Peel, D. (2004). Finite Mixture Models. New York: John Wiley & Sons.Google Scholar
Meng, X.L. & Rubin, D.B. (1993). Maximum likelihood estimation via the ECM algorithm: a general framework. Biometrika, 80(2), 267–278. ISSN 0006-3444.CrossRefGoogle Scholar
Miljkovic, T. & Grün, B. (2016). Modeling loss data using mixtures of distributions. Insurance: Mathematics and Economics, 70, 387–396. ISSN 0167-6687.Google Scholar
Scollnik, D.P. & Sun, C. (2012). Modeling with Weibull-Pareto models. North American Actuarial Journal, 16(2), 260–272.CrossRefGoogle Scholar
Tseung, S.C., Badescu, A.L., Fung, T.C. & Lin, X.S. (2020). LRMoE: an R package for flexible actuarial loss modelling using mixture of experts regression model. Available in SSRN: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3740215CrossRefGoogle Scholar
Yin, C. & Lin, X.S. (2016). Efficient estimation of Erlang mixtures using iSCAD penalty with insurance application. ASTIN Bulletin: The Journal of the IAA, 46(3), 779–799.CrossRefGoogle Scholar