The Effect of a Threshold Proportional Reinsurance Strategy on Ruin Probabilities

In the context of a compound Poisson risk model, we define a threshold proportional reinsurance strategy: A retention level k1 is applied whenever the reserves are less than a determinate threshold b, and a retention level k2 is applied in the other case. We obtain the integro-differential equation for the Gerber-Shiu function (defined in Gerber and Shiu (1998)) in this model, which allows us to obtain the expressions for ruin probability and Laplace transforms of time of ruin for several distributions of the claim sizes. Finally, we present some numerical results.time of ruin, threshold proportional reinsurance strategy, ruin probability, gerber-shiu function

Implementing PLS for distance-based regression: computational issues

Distance-based regression allows for a neat implementation of the Partial Least Squares recurrence. In this paper we address practical issues arising when dealing with moderately large datasets (n ~ 10^4) such as those typical of automobile insurance premium calculations

Time of ruin in a risk model with generalized Erlang (n) interclaim times and a constant dividend barrier

In this paper we analyze the time of ruin in a risk process with the interclaim times being Erlang(n) distributed and a constant dividend barrier. We obtain an integro-differential equation for the Laplace Transform of the time of ruin. Explicit solutions for the moments of the time of ruin are presented when the individual claim amounts have a distribution with rational Laplace transform. Finally, some numerical results and a compare son with the classical risk model, with interclaim times following an exponential distribution, are given.risk theory, constant dividend barrier, laplace transform, time of ruin, generalized erlang (n) distribution

IMPLEMENTING PLS FOR DISTANCE-BASED REGRESSION: COMPUTATIONAL ISSUES

Distance-based regression allows for a neat implementation of the Partial Least Squares recurrence. In this paper we address practical issues arising when dealing with moderately large datasets (n ~ 104) such as those typical of automobile insurance premium calculations.

Bootstrapping pairs in Distance-Based Regression

Distance-based regression is a prediction method consisting of two steps: from distances between observations we obtain latent variables which, in turn, are the regressors in an ordinary least squares linear model. Distances are computed from actually observed predictors by means of a suitable dissimilarity function. Being in general nonlinearly related with the response their selection by the usual F tests is unavailable. In this paper we propose a solution to this predictor selection problem, by defining generalized test statistics and adapting a non-parametric bootstrap method to estimate their p-values. We include a numerical example with automobile insurance data.non-parametric bootstrap, automobile insurance data, predictors selection, distance-based regression

Discrete analysis of dividend payments in a non-life insurance portfolio

The process of free reserves in a non-life insurance portfolio as defined in the classical model of risk theory is modified by the introduction of dividend policies that set maximum levels for the accumulation of reserves. The first part of the work formulates the quantification of the dividend payments via the expectation of their current value under different hypotheses. The second part presents a solution based on a system of linear equations for discrete dividend payments in the case of a constant dividend barrier, illustrated by solving a specific case.dividend policies, expected present value

Solvabilité II

Selon l’Autorité Européenne des Assurances et des Pensions Professionnelles (AEAPP) (European Insurance and Occupational Pensions Authority (EIOPA), en anglais), “Solvabilité II est un projet qu’a comme objectif réviser le régime de surveillance des entreprises d’assurance et réassurance dans l’Union Européenne. Le premier pas a été l’adoption en Novembre de 2009 de la Directive Solvabilité II.” Ce document présente les concepts clés et les principales formules de calcul quantitatif inclus dans Solvabilité II. Ce document est le résultat de la préparation et l’enseignement du point 4 du cours «Solvabilité» du Master en Sciences Actuarielles et Financières de l’Université de Barcelone. Cette version en français est le résultat de la participation dans la “Formation des formateurs” en collaboration avec l’ISFA de l’Université de Lyon-I

Equilibrium distributions and discrete Schur-constant models

This paper introduces Schur-constant equilibrium distribution models of dimension n for arithmetic non-negative random variables. Such a model is defined through the (several orders) equilibrium distributions of a univariate survival function. First, the bivariate case is considered and analyzed in depth, stressing the main characteristics of the Poisson case. The analysis is then extended to the multivariate case. Several properties are derived, including the implicit correlation and the distribution of the sum

Time of ruin in a risk model with generalized Erlang (n) interclaim times and a constant dividend barrier

In this paper we analyze the time of ruin in a risk process with the interclaim times being Erlang(n) distributed and a constant dividend barrier. We obtain an integro-differential equation for the Laplace Transform of the time of ruin. Explicit solutions for the moments of the time of ruin are presented when the individual claim amounts have a distribution with rational Laplace transform. Finally, some numerical results and a compare son with the classical risk model, with interclaim times following an exponential distribution, are given.En este artículo analizamos el momento de ruina en un proceso del riesgo donde el tiempo de ocurrencia entre los siniestros se distribuye según una Erlang(n) y con una barrera de dividendos constate. Obtenemos una ecuación integro diferencial para la Transformada de Laplace del momento de ruina. Presentamos soluciones explicitas para el momento de ruina cuando la cuantía individual de un siniestro cumple que la Transformada de Laplace de su función distribución es racional. Finalmente, se muestran resultados numéricos y una comparación con el modelo clásico (con tiempos de interocurrencia exponencial)En aquest article analitzem el moment de ruïna en un procés del risc on el temps d'ocurrència entre els sinistres es distribuïx segons uneixi Erlang(n) i amb una barrera de dividends constati. Obtenim una equació integro diferencial per a la Transformada de Laplace del moment de ruïna. Presentem solucions explicites per al moment de ruïna quan la quantia individual d'un sinistre complix que la Transformada de Laplace de la seva funció distribució és racional. Finalment, es mostren resultats numèrics i una comparança amb el model clàssic (amb temps de interocurrencia exponencial

Is a Refundable Deductible Insurance an Advantage for the Insured? A Mathematical Approach

Most insurance policies include a deductible, so that a part of the claim is paid by the insured. In order to get full coverage of the claim, the insured has two options: purchase a Zero Deductible Insurance Policy or purchase an insurance policy with deductible together with Refundable Deductible Insurance. The objective of this paper is to analyze these two options and compare the premium paid by each. We define dif(P) as the difference between the premiums paid. This function depends on the parameters of the deductible applied, and we focus our attention on the sign of this difference and the calculation of the optimal deductible, that is, the values of the parameters of the deductible that allow us to obtain the greatest reduction in the premium