Mixture Distributions in a Heterogeneous Portfolio of Policies

• Autorzy: Viera Pacakova
• Języki publikacji: EN

Abstrakty

EN

The concept of a mixture of distributions is an important one in insurance, since insurance companies generally deal with heterogeneous risks. The simplest model for the number of claims is the Poisson model, so we assume that the number of claims N_i made by policyholder i follows the Poisson distribution with mean λ_i. We know that the values of λ_i will vary across the portfolio. We take distribution gamma as the mixing distribution for the Poisson means and show that the marginal distribution of the number of claims is negative binomial. In second example we suppose that each individual in a large insurance portfolio incurs losses according to its own exponential distribution, i.e. the exponential distributions have means which differ from individual to individual. Our purpose is to describe the losses over the whole portfolio. We show that the mixture distribution is Pareto when exponentially distributed losses are averaged using a gamma mixing distribution. (fragment of text)

Słowa kluczowe

EN

Insurances; Moments of gamma distribution

PL

Ubezpieczenia; Momenty rozkładu gamma

• Czasopismo: Prace Naukowe Akademii Ekonomicznej we Wrocławiu
• Rocznik: 2002
• Numer: nr 952 Inwestycje finansowe i ubezpieczenia - tendencje światowe a polski rynek
• Strony: 41--44

Twórcy

autor

Viera Pacakova

• University of Economics in Bratislava, Slovakia

Bibliografia

• Currie I.D.: Loss Distributions. Institute of Actuaries and Faculty of Actuaries, London and Edinburgh, 1993.
• Dickson D.C.M., Waters H.R.: Risk models. Institute of Actuaries and Faculty of Actuaries, London and Edinburgh, 1993.
• Hogg, R.V., Klugman S.A.: Loss Distributions. John Wiley & Sons, New York, 1984.
• Pacáková V.: Štatistika pre poistnú prax. STATIS Bratislava, 1999.
• Pacáková V.: Mixture Distributions and Variability in a Heterogeneous Portfolio of Policies. Proceedings of the Seminar Statistical Methods in Socioeconomic Researches - Theory and Applications, Krakow 2000.