226 research outputs found
Un caso particolare di rovina in tempi finiti
No full textSi esamina l’equazione di Arfwedson per il calcolo della probabilità di non rovina in tempi finiti nell’ipotesi di assenza di entrate. Considerando un processo stocastico dei sinistri Poisson composto si studia il caso in cui le somme a rischio seguano una distribuzione mistura di un’esponenziale e di una Erlang(1). Per la predetta probabilità di non rovina si trova un’espressione esplicita e la si esprime tramite serie convolutoria
Credibilità e GLM per la tariffazione con variabili multilivello
No full textThe use of GLMs is often combined with the use of other actuarial techniques. In this paper we consider the use of GLMs combined with credibility methods in ratemaking with multilevel variables. Recent contributions to the literature are reviewed
Generalized Linear Mixed Models for Claims Reserving and the Bornhuetter-Ferguson Method
No full textWe consider a Generalized Linear Mixed Model for claims reserving with the aim of taking account of external information, besides the usual data given by a claims development triangle of observations. The external data are incorporated into the model by connecting them with the random effects. A numerical example is provided
La classe bonus-malus come variabile esplicativa nella tariffazione R.C.A.
No full textUn problema che si presenta nella tariffazione a priori dei rischi RCA in presenza di sistemi bonus-malus (BM) riguarda il modo di trattare l'informazione sulla classe BM di appartenenza. La difficoltà a trovare una risposta alla precedente domanda deriva dal fatto che la classe BM riassume informazioni che si ottengono a posteriori; d'altro canto essa racchiude significative informazioni sulla sinistrosità. In questo lavoro, prendendo come riferimento metodologico il modello di aggiornamento Bayesiano, vengono analizzati alcuni aspetti del problema, tra i quali: la determinazione di relatività adeguate per valutare l'effetto sulla sinistrosità delle caratteristiche rilevabili a priori; le implicazioni legate all'introduzione della classe BM come variabile esplicativa
Velikie Minei Čet'i mitropolita Moskosvkogo i vseja Rusi Makarija
No full textВ статье рассматривается книжный памятник – Великие Минеи Четьи как собрание, состоящее из 12 рукописных книг и объединяющее огромный книжный свод XVI века: древнерусские оригинальные и переводные памятники, главным образом житийные и риторические, духовно‐учительного, церковно‐ повествовательного и исторического характера. В ходе аналитического описания автор доказывает, что Великие Минеи Четьи стали своего рода энциклопедией древнерусской духовной книжности XVIвека. Более подробно автор рассматривает «Житие Георгия Нового»: историю его составления, агиографические источники и филологические проблемы, связанные с этим летописным текстом.The article discusses the book Great monument to lives of Saints as a collection consisting of 12 handwritten books and combines a huge book set of the 16th century: original and translated ancient monuments, mostly narrative and rhetorical, spiritual teaching, of Church‐narrative and historical character. During the analytical description the author proves that the great Menaion reader Lives have become a kind of encyclopedia of ancient spiritual literature of the 16th century. The author examines in more detail «The Life of George the New»: a history of its drafting, hagiographic sources and philological problems related to Chronicle text
Robustness and consistency of parametric risk measures under normality: theory and an application to proportional reinsurance
No full textWe introduce the idea of parametric risk measure and discuss properties of robustness of the risk based preferences and of consistency of these with the usual standard deviation based preferences. Furthermore, we analyze robustness and consistency of mean-risk dominance relation and mean-risk efficient set, providing necessary and sufficient conditions for robustness and consistency of the efficient set generated by the parametric risk measure associated to the W-ruin probability. Among other things, this allows an enlightening re-reading, of the ground breaking de Finetti’s paper on variable quota share proportional reinsurance
The Bornhuetter-Ferguson Claims Reserving Method and Generalized Linear Models
No full textIn the actuarial practice, the Bornhuetter-Ferguson (BF) method is commonly used to combine external estimates of the expected ultimate claims with data of a run-off triangle of payments. The BF claims reserve of each accident year is proportional to the external estimates. The coefficients of proportionality depend on the claims development pattern and are usually estimated by the Chain-ladder technique. Mack (2006) criticizes this solution and proposes different estimates.
In this paper we tackle the problem in the framework of Generalized Linear Models (GLM), where the external estimates can be incorporated by means of offset terms. We show that a particular GLM allows obtaining the estimates of the claims development pattern suggested by Mack. Within the GLM framework we can easily calculate prediction errors to evaluate the uncertainty connected with the estimates of the claims development pattern. By simulation we can also evaluate the uncertainty due to the external estimate of the ultimate claims
Credibility and HGLM in claims reserving
No full textA Tweedie regression model with random effects is applied to claims reserving in general insurance. The parameter estimates are obtained by following two different approaches: the one in Ohlsson, Johansson (2006), which combines generalized linear models with credibility, and the hierarchical generalized linear models approach (Lee, Nelder (2001)). In both cases the claims reserves and the estimation errors are evaluated. A numerical example illustrates the two approaches
Un procedimento di risoluzione dell’equazione integro-differenziale di Gerber-Shiu
No full textNell’ambito del modello classico della teoria del Rischio, con un processo dei sinistri poissoniano, troviamo una soluzione analitica dell’equazione integro-differenziale di Gerber-Shiu nell’ipotesi in cui la distribuzione delle somme a rischio sia una Erlang riconducendo il problema alla risoluzione di un’equazione differenziale
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