XREAP2011-06:Estimation of Parametric and Nonparametric Models for Univariate Claim Severity Distributions – an approach using R

This paper presents an analysis of motor vehicle insurance claims relating to vehicle damage and to associated medical expenses. We use univariate severity distributions estimated with parametric and non-parametric methods. The methods are implemented using the statistical package R. Parametric analysis is limited to estimation of normal and lognormal distributions for each of the two claim types. The nonparametric analysis presented involves kernel density estimation. We illustrate the benefits of applying transformations to data prior to employing kernel based methods. We use a log-transformation and an optimal transformation amongst a class of transformations that produces symmetry in the data. The central aim of this paper is to provide educators with material that can be used in the classroom to teach statistical estimation methods, goodness of fit analysis and importantly statistical computing in the context of insurance and risk management. To this end, we have included in the Appendix of this paper all the R code that has been used in the analysis so that readers, both students and educators, can fully explore the techniques described.

Pitt, D.; Guillén, M. (RFA-IREA); Bolancé, C. (RFA-IREA)

XREAP2011-06.pdf

XREAP2011-08: Loss risk through fraud in car insurance

Our objective is to analyse fraud as an operational risk for the insurance company. We study the effect of a fraud detection policy on the insurer’s results account, quantifying the loss risk from the perspective of claims auditing. From the point of view of operational risk, the study aims to analyse the effect of failing to detect fraudulent claims after investigation. We have chosen VAR as the risk measure with a non-parametric estimation of the loss risk involved in the detection or non-detection of fraudulent claims. The most relevant conclusion is that auditing claims reduces loss risk in the insurance company.

Ayuso, M. (RFA-IREA); Guillén, M. (RFA-IREA); Bolancé, C. (RFA-IREA)

XREAP2011-08.pdf

XREAP2011-09:The link between public support and private R&D effort: What is the optimal subsidy?

The effectiveness of R&D subsidies can vary substantially depending on their characteristics. Specifically, the amount and intensity of such subsidies are crucial issues in the design of public schemes supporting private R&D. Public agencies determine the intensities of R&D subsidies for firms in line with their eligibility criteria, although assessing the effects of R&D projects accurately is far from straightforward. The main aim of this paper is to examine whether there is an optimal intensity for R&D subsidies through an analysis of their impact on private R&D effort. We examine the decisions of a public agency to grant subsidies taking into account not only the characteristics of the firms but also, as few previous studies have done to date, those of the R&D projects. In determining the optimal subsidy we use both parametric and nonparametric techniques. The results show a non-linear relationship between the percentage of subsidy received and the firms’ R&D effort. These results have implications for technology policy, particularly for the design of R&D subsidies that ensure enhanced effectiveness.

Duch-Brown, N. (IEB); García-Quevedo, J. (IEB); Montolio, D. (IEB)

XREAP2011-09.pdf

XREAP2011-10: Mixture of bivariate Poisson regression models with an application to insurance

In a recent paper Bermúdez [2009] used bivariate Poisson regression models for ratemaking in car insurance, and included zero-inflated models to account for the excess of zeros and the overdispersion in the data set. In the present paper, we revisit this model in order to consider alternatives. We propose a 2-finite mixture of bivariate Poisson regression models to demonstrate that the overdispersion in the data requires more structure if it is to be taken into account, and that a simple zero-inflated bivariate Poisson model does not suffice. At the same time, we show that a finite mixture of bivariate Poisson regression models embraces zero-inflated bivariate Poisson regression models as a special case. Additionally, we describe a model in which the mixing proportions are dependent on covariates when modelling the way in which each individual belongs to a separate cluster. Finally, an EM algorithm is provided in order to ensure the models’ ease-of-fit. These models are applied to the same automobile insurance claims data set as used in Bermúdez [2009] and it is shown that the modelling of the data set can be improved considerably.

Bermúdez, Ll. (RFA-IREA); Karlis, D.

XREAP2011-10.pdf

XREAP2011-11: Age effects, unobserved characteristics and hedonic price indexes: The Spanish car market in the 1990s

This paper computes and compares alternative quality-adjusted price indexes for new cars in Spain in the period 1990-2000. The proposed hedonic approach simultaneously controls for time-invariant unobserved product e¤ects and time-variant unobserved quality changes, that are assumed to be captured by model age e¤ects. The results show that the non-adjusted price index largely overstates the increase in the cost of living induced by changes in car prices and that previous evidence for this market have not measured the real extent of that bias, probably due to the omission of controls for unobservables. It is also shown that omitting age e¤ects can also lead to misleading conclusions. The estimated price indexes give also some insights on what could have been the determinants of price evolution in the Spanish car market.

Varela-Irimia, X-L. (GRIT)

XREAP2011-11.pdf

XREAP2011-12: A correlation sensitivity analysis of non-life underwriting risk in solvency capital requirement estimation

This paper analyses the impact of using different correlation assumptions between lines of business when estimating the risk-based capital reserve, the Solvency Capital Requirement (SCR), under Solvency II regulations. A case study is presented and the SCR is calculated according to the Standard Model approach. Alternatively, the requirement is then calculated using an Internal Model based on a Monte Carlo simulation of the net underwriting result at a one-year horizon, with copulas being used to model the dependence between lines of business. To address the impact of these model assumptions on the SCR we conduct a sensitivity analysis. We examine changes in the correlation matrix between lines of business and address the choice of copulas. Drawing on aggregate historical data from the Spanish non-life insurance market between 2000 and 2009, we conclude that modifications of the correlation and dependence assumptions have a significant impact on SCR estimation.

Bermúdez, Ll. (RFA-IREA), Ferri, A. (RFA-IREA), Guillén, M. (RFA-IREA)

XREAP2011-12.pdf

XREAP2011-13: A logistic regression approach to estimating customer profit loss due to lapses in insurance

This article focuses on business risk management in the insurance industry. A methodology for estimating the profit loss caused by each customer in the portfolio due to policy cancellation is proposed. Using data from a European insurance company, customer behaviour over time is analyzed in order to estimate the probability of policy cancelation and the resulting potential profit loss due to cancellation. Customers may have up to two different lines of business contracts: motor insurance and other diverse insurance (such as, home contents, life or accident insurance).  Implications for understanding customer cancellation behaviour as the core of business risk management are outlined.

Guillén, M. (RFA-IREA); Pérez-Marín, A. M. (RFA-IREA); Alcañiz, M. (RFA-IREA)

XREAP2011-13.pdf

XREAP2011-14: Evaluation of subsidies programs to sell green cars: Impact on prices, quantities and efficiency

During the recent period of economic crisis, many countries have introduced scrappage schemes to boost the sale and production of vehicles, particularly of vehicles designed to pollute less. In this paper, we analyze the impact of a particular scheme in Spain (Plan2000E) on vehicle prices and sales figures as well as on the reduction of polluting emissions from vehicles on the road. We considered the introduction of this scheme an exogenous policy change and because we could distinguish a control group (non-subsidized vehicles) and a treatment group (subsidized vehicles), before and after the introduction of the Plan, we were able to carry out our analysis as a quasi-natural experiment. Our study reveals that manufacturers increased vehicle prices by the same amount they were granted through the Plan (1,000 €). In terms of sales, econometric estimations revealed an increase of almost 5% as a result of the implementation of the Plan. With regard to environmental efficiency, we compared the costs (inverted quantity of money) and the benefits of the program (reductions in polluting emissions and additional fiscal revenues) and found that the Plan would only be beneficial if it boosted demand by at least 30%.

Jiménez, J. L.; Perdiguero, J. (GiM-IREA); García, C.

XREAP2011-14.pdf

XREAP2011-15: A New Open Economy Macroeconomic Model with Endogenous Portfolio Diversifi…cation and Firms Entry

This paper provides a new benchmark for the analysis of the international diversi…cation puzzle in a tractable new open economy macroeconomic model. Building on Cole and Obstfeld (1991) and Heathcote and Perri (2009), this model speci…es an equilibrium model of perfect risk sharing in incomplete markets, with endogenous portfolios and number of varieties. Equity home bias may not be a puzzle but a perfectly optimal allocation for hedging risk. In contrast to previous work, the model shows that: (i) optimal international portfolio diversi…cation is driven by home bias in capital goods, independently of home bias in consumption, and by the share of income accruing to labour. The model explains reasonably well the recent patterns of portfolio allocations in developed economies; and (ii) optimal portfolio shares are independent of market dynamics.

Arespa, M. (CREB)

XREAP2011-15.pdf