A practitioners approach to individual claims models for bodily injury claims in german non-life insurance

The aim of our paper is to discuss the difficulties non-life actuaries are currently facing from a practical point of view. Based on this, we show that individual claims models are the key to address these difficulties and discuss how such models give actuaries a new and very powerful tool to explore further fields of application. Moreover, we address a very essential question: What data is needed for developing individual claims models? For bodily injury claims in German motor liability insurance, we shall derive specific attributes based on a detailed discussion of the legal background. All our ideas are based on practical experience for a large German motor insurance portfolio.

A NEW MULTIVARIATE ZERO-INFLATED HURDLE MODEL WITH APPLICATIONS IN AUTOMOBILE INSURANCE

The fact that a large proportion of insurance policyholders make no claims during a one-year period highlights the importance of zero-inflated count models when analyzing the frequency of insurance claims. There is a vast literature focused on the univariate case of zero-inflated count models, while work in the area of multivariate models is considerably less advanced. Given that insurance companies write multiple lines of insurance business, where the claim counts on these lines of business are often correlated, there is a strong incentive to analyze multivariate claim count models. Motivated by the idea of Liu and Tian (Computational Statistics and Data Analysis, 83, 200–222; 2015), we develop a multivariate zero-inflated hurdle model to describe multivariate count data with extra zeros. This generalization offers more flexibility in modeling the behavior of individual claim counts while also incorporating a correlation structure between claim counts for different lines of insurance business. We develop an application of the expectation–maximization (EM) algorithm to enable the statistical inference necessary to estimate the parameters associated with our model. Our model is then applied to an automobile insurance portfolio from a major insurance company in Spain. We demonstrate that the model performance for the multivariate zero-inflated hurdle model is superior when compared to several alternatives.

Mixed Poisson Regression Models with Varying Dispersion Arising from Non-Conjugate Mixing Distributions

In this article we present a class of mixed Poisson regression models with varying dispersion arising from non-conjugate to the Poisson mixing distributions for modelling overdispersed claim counts in non-life insurance. The proposed family of models combined with the adopted modelling framework can provide sufficient flexibility for dealing with different levels of overdispersion. For illustrative purposes, the Poisson-lognormal regression model with regression structures on both its mean and dispersion parameters is employed for modelling claim count data from a motor insurance portfolio. Maximum likelihood estimation is carried out via an expectation-maximization type algorithm, which is developed for the proposed family of models and is demonstrated to perform satisfactorily.

Approximate Valuation of Life Insurance Portfolio with the Cluster Analysis: Trade-Off Between Computation Time and Precision

Valuation of the insurance portfolio is one of the essential actuarial tasks. Life insurance valuation is usually based on a projection of cash flows for each policy which is demanding computation time. Furthermore, modern financial management requires multiple valuations under different scenarios or input parameters. A method to reduce computation time while preserving as much accuracy as possible based on cluster analysis is presented. The basic idea of the method is to replace the original portfolio by a smaller representative portfolio based on clusters with some weights that would ensure the similarity of the valuation results to the original portfolio. Valuation is then significantly faster but requires initial time for clustering and the results are only approximate – different from the original results. The difference is studied for a different number of clusters and the trade-off between the approximation error and calculation time is evaluated.

Contributions from Spatial Models to Non-Life Insurance Pricing: An Empirical Application to Water Damage Risk

This paper explores the application of spatial models to non-life insurance data focused on the multi-risk home insurance branch. In the pricing modelling and rating process, spatial information should be considered by actuaries and insurance managers because frequencies and claim sizes may vary by region and the premium should be different considering this rating variable. In addition, it is relevant to examine the spatial dependence due to the fact that the frequency of claims in neighbouring regions is often expected to be more closely related than those in regions far from each other. In this paper, a comparison between spatial models, such as spatial autoregressive models (SAR), the spatial error model (SEM), and the spatial Durbin model (SDM), and a non-spatial model has been developed. The data used for this analysis are for a home insurance portfolio located in Spain, from which we have selected peril of water coverage.

Modeling the Future Value Distribution of a Life Insurance Portfolio

This paper addresses the problem of approximating the future value distribution of a large and heterogeneous life insurance portfolio which would play a relevant role, for instance, for solvency capital requirement valuations. Based on a metamodel, we first select a subset of representative policies in the portfolio. Then, by using Monte Carlo simulations, we obtain a rough estimate of the policies’ values at the chosen future date and finally we approximate the distribution of a single policy and of the entire portfolio by means of two different approaches, the ordinary least-squares method and a regression method based on the class of generalized beta distribution of the second kind. Extensive numerical experiments are provided to assess the performance of the proposed models.

Global Index on Financial Losses Due to Crime in the United States

Despite the potential importance of crime rates in investments, there are no indices dedicated to evaluating the financial impact of crime in the United States. As such, this paper presents an index-based insurance portfolio for crime in the United States by utilizing the financial losses reported by the Federal Bureau of Investigation. The objective of our paper is to introduce new risk hedging financial contracts for crime, consistent with dynamic asset pricing. Underlying the index, we hedge the investments by issuing marketable European call and put options and providing risk budgets. These budgets show that real estate, ransomware, and government impersonation are the main risk contributors in our index. Next, we evaluate the performance of our index via stress testing to determine its resilience to economic crisis. Of all the factors considered in this study, unemployment rate has the potential to demonstrate the highest systemic risk to the portfolio. Our portfolio will help investors envision risk exposure in the market, gauge investment risk based on their desired risk level, and hedge strategies for potential losses due to economic crashes. In conclusion, we provide a basis for the securitization of insurance risk from certain crimes that could forewarn investors to transfer their risk to capital market investors.

THE PROBLEMS OF THE DOMESTIC REINSURANCE DEVELOPMENT IN CONDITIONS OF FINANCIAL INSTABILITY

Financial instability stems from the excessive volatility in the financial markets, the weakness of financial institutions and the inability of financial sector companies to fulfill their obligations, and it is no exception to insurance companies that do not have sufficient financial resources to reinsure. In modern conditions, reinsurance provides stability to the development of the insurers and is one of the most important tools that provides effective protection against various natural, man-made and other risks. The lack of financial resources of the insurance companies objectively determines the limitations of their ability to insure large risks. Reinsurance enables the insurance companies, by attracting funds from other insurers, to ensure the honest fulfillment of their obligations to insure payment at the onset of an insured event, while maintaining the stability of their financial situation. Admission to the insurance of expensive objects is dangerous for the individual insurer’s financial stability through the coverage of losses in the insured event. Admission to the insurance of expensive objects is dangerous for the individual insurer’s financial stability through the coverage of losses in the insured event. The need for reinsurance is due, among other things, to regulatory requirements for capital and assets and provides tools for rapid development of the insurance portfolio. Simultaneously reinsurance enables to protect the insurance portfolio from the influence on it of a series of large insurance risks, including catastrophic, so that the payment of insurance compensations on them does not pose a heavy burden on the one insurance company, but is carried out collectively by all participants in reinsurance. As a result, reinsurance allows you to take insurance risks that far outweigh the insurer’s own financial resources. Thus, the reinsurance system is a guarantee of financial stability of any insurance company, providing protection of its capital, and the basis for increasing the volume and quality of insurance services. In Article, the essence and significance of reinsurance in the conditions of globalization of the world economy were considered, as well as analysis of the main tendencies of the domestic reinsurance market development and the problems of its development in Ukraine were revealed. Keywords: insurance, financial instability, volatility, financial market, reinsurance, commission remuneration. JEL Classification E44, G20, G22, O16 Formulas: 0; fig.: 2; tabl.: 4; bibl.: 15.

EVALUATION OF INSURANCE PORTFOLIO

The article discusses the peculiarities of forming a balanced insurance portfolio and a system of indicators of the insurance organization's portfolio assessment. The main features of the balanced insurance portfolio and the essence of its main indicators are considered: the number of objects in the portfolio, the maximum insurance amount of own maintenance under the agreements in force for the period in question, the indicator of the uniformity of the portfolio and the equilibrium coefficient of the insurance portfolio, the estimated insurance portfolio, the expected return of the insurance portfolio and profitability by types of insurance transactions. It is noted that the optimization of the insurance portfolio is understood as reducing the level of risk and increasing the financial stability of the portfolio. The practical value of the research lies in the formation of an insurance portfolio assessment system.

ON THE FAMILY OF DISTRIBUTIONS WITH ACTUARIAL APPLICATIONS

ABSTRACT In this paper, a new three-parameter discrete family of distributions, the $$r{\cal B}ell$$ family, is introduced. The family is based on series expansion of the r-Bell polynomials. The proposed model generalises the classical Poisson and the recently proposed Bell and Bell–Touchard distributions. It exhibits interesting stochastic properties. Its probabilities can be computed by a recursive formula that allows us to calculate the probability function of the amount of aggregate claims in the collective risk model in terms of an integral equation. Univariate and bivariate regression models are presented. The former regression model is used to explain the number of out-of-use claims in an automobile insurance portfolio, by showing a good out-of-sample performance. The latter is used to describe the number of out-of-use and parking claims jointly. This family provides an alternative to other traditionally used distributions to describe count data such as the negative binomial and Poisson-inverse Gaussian models.