Dependence may arise in insurance when the insureds are clustered into groups e.g. joint-life annuities. This dependence may be produced by sharing a common risk acting on mortality of members of the group. Various dependence models have been considered in literature; however, the focus has been on either the lower-tail dependence alone or upper-tail dependence alone. This article implements the frailty dependence approach to life insurance problems where most applications have been within medical setting. Our strategy is to use the conditional independence assumption given an observed association measure in a positive stable frailty approach to account for both lower and upper-tail dependence. The model is calibrated on the association of Kenyan insurers 2010 male and female published rates. The positive stable model is then proposed to construct dependence life-tables and generate life annuity payment streams in the competitive Kenyan market.

Dans ce papier, nous proposons un estimateur de la classe de mesures de la pauvreté de Foster, Greer et Thorbecke. Le nouveau estimateur est construit avec un noyau adaptatif et la largeur de fenêtre de l'estimateur amélioré est obtenue en fonction de l'étendue des observations. Un exemple de simulation est présenté permettant de faire des comparaisons avec quatre autres estimateurs. La performance du nouveau estimateur proposé est évaluée au moyen de la variance et du critère de l'erreur quadratique moyenne. Les résultats de l'étude de simulation sont très prometteurs; ils montrent que notre estimateur modifié se comporte bien dans tous les cas.

Grouping insureds in clusters such as joint-life annuities imposes statistical dependence. In this paper, we propose the shared compound frailty approach in collective valuation of joint-life annuity products where most applications have been in bio-statistics. The positive stable compound process used entails the frailty mixing distribution with the weighted exponential, generalized exponential and weighted Weibull as the base force of mortality distributions calibrated on a large Kenyan insurer joint-life last-survivor dataset. The findings shows that the positive stable generalized exponential model addresses time-varying heterogeneity effects positively and negatively associated with dependence

Insurance of chronic illness is slowly gaining ground in Kenya which has lead to insurance firms introducing insurance products of chronic illness among them being cancer insurance policies. However, unlike other chronic illnesses, cancer can move from the organ of origin to another which will consequently lead to increased cost of treatment. This can not be modeled using ordinary distributions hence it has become an area of interest for many researchers. Zero-truncated phase type distributions are used to solve this drawback of ordinary distributions as it can in-cooperate these transitions while modeling claim count data. They further improve modeling of claim count data as they only consider positive values of claim count excluding zeros. This is the nature of real claim count data as zero claim frequency can not attract any claim severity amount. In this paper aggregate claim losses of secondary cancers in Kenya are estimated using Zero-truncated Poisson Lindley distributions. Zero-truncated one parameter as well as Zero-truncated two parameter Poisson Lindley distributions are derived. Their compound probability generating functions are also constructed. The transitions states of secondary cancer states are estimated using continuous Chapman Kolmogorov equation and used as the matrix parameters for the claim count distributions. Pareto, Generalized Pareto, Weibull, OPPL and TPPL distributions are the distributions considered in this research in modeling claim numbers. This study concludes that aggregate losses of secondary cancer cases using Kenyan data are best modeled by PH-ZTOPPL Generalized Pareto model for PH-ZTOPPL distribution models while for PH-ZTTPPL distribution models the best model was PH-ZTTPPL-Generalized Pareto model. The two best models were compared and PH-ZTTPPL-Generalized Pareto model was proven to be the best model. Comparing this model with PH-TPPL Generalized Pareto model from earlier research PH-TPPL Generalized Pareto model proved to be a better model implying that zero claim count data should be considered in estimation of aggregate losses

L'assurance des maladies chroniques dont le cancer gagne du terrain au Kenya peu à peu. Ce pendant le traitement de ces maladies, pouvant entrainer des changements d'organes humains, tend à coûter plus cher, et en conséquence, à augmenter les primes d'assurance notablement. La modélisation de ces primes ne peut plus se faire avec des distributions ordinaires. Les méthodes utilisant des distributons zero-tronquées sont utilisées en particulier. Dans ce papier, elles sont utilisées en rapport avec des distributions Pareto, Weibul etc. Nous procédons à une comparaison de ces distributions et en proposons deux qui sont les meilleures