Spatial modelling of claim frequency and claim size in non-life insurance
Abstract
In this paper, models for claim frequency and average claim size in non-life insurance are considered. Both covariates and spatial random effects are included allowing the modelling of a spatial dependency pattern. We assume a Poisson model for the number of claims, while claim size is modelled using a Gamma distribution. However, in contrast to the usual compound Poisson model, we allow for dependencies between claim size and claim frequency. A fully Bayesian approach is followed, parameters are estimated using Markov Chain Monte Carlo (MCMC). The issue of model comparison is thoroughly addressed. Besides the deviance information criterion and the predictive model choice criterion, we suggest the use of proper scoring rules based on the posterior predictive distribution for comparing models. We give an application to a comprehensive data set from a German car insurance company. The inclusion of spatial effects significantly improves the models for both claim frequency and claim size, and also leads to more accurate predictions of the total claim sizes. Further, we detect significant dependencies between the number of claims and claim size. Both spatial and number of claims effects are interpreted and quantified from an actuarial point of view.
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Empirical studies show that claim counts and amounts are often dependent and negatively correlated in auto and health insurance.
“In practice, empirical studies show that claim counts and amounts are often dependent and negatively correlated in auto and health insurance (see, e.g., Frees et al. 2011; Garrido et al. 2016; Gschlößl and Czado 2007; Shi et al. 2015).”
From Modelling Motor Insurance Claim Frequency and Severity Using Gradient Boosting (2023) · cites this paper as Gschlößl and Czado 2007
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- Authors
- Gschlößl, S., & Czado, C.
- Affiliations
- Technical University of Munich (DE)
- Corresponding author
- Czado, Claudia
- ORCID
- Czado, Claudia
- Venue
- Scandinavian Actuarial Journal
- Publisher
- Informa UK Limited
- Published
- 2007-09
- Volume
- 2007
- Issue
- 3
- Pages
- 202-225
- ISSN
- 0346-1238 (ISSN-L)
- 1651-2030
- OpenAlex
- W1988427103
- Cited by
- 96
- References
- 29
- Citations by year
- 2026: 2 · 2025: 5 · 2024: 7 · 2023: 5 · 2022: 10 · 2021: 9 · 2020: 12 · 2019: 10 · 2018: 3 · 2017: 3 · 2016: 6 · 2015: 6 · 2014: 4 · 2013: 5 · 2012: 2
- FWCI
- 1.91
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Scandinavian Actuarial Journal (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Probability and Risk Models
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Insurance and Financial Risk Management
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Spatial and Panel Data Analysis
- Keywords
- non-life insurance, claim frequency, claim size, spatial random effects, spatial dependence, Poisson-gamma model, compound Poisson model, Bayesian model selection, proper scoring rules, posterior predictive distribution, automobile insurance, actuarial modeling
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