Automatic balance mechanisms for notional defined contribution pension systems guaranteeing social adequacy and financial sustainability: an application to the Italian pension system

Since the mid 1990s some European countries (including Italy) implemented a Notional Defined Contribution (NDC) pension system. Such a system is based on pay-as-you-go funding, while the pension amount is a function of the individual lifelong contribution. Despite many appealing features, the NDC system presents some drawbacks: first, it is vulnerable to demographic and economic shocks compromising the financial sustainability; second, it could fail to guarantee adequate pension benefits to pensioners. In order to reduce the first limit, automatic balance mechanisms (ABMs) have been proposed in literature and also implemented in Sweden, while solutions that combine financial sustainability and social adequacy have been applied only in a pay-as-you-go point system. The aim of this paper is to insert into the Italian NDC architecture ABMs that preserve social adequacy under financial sustainability constraints. Godinez-Olivares et al. (Insur Math Econ 69:117–126, 2016) built ABMs for a Defined Benefit pension system using nonlinear optimization techniques to calculate the optimal paths of the control variables representing the main drivers of the system: contribution rate, retirement age and indexation of pensions. Following this line of research, we have developed a nonlinear optimization model for the Italian NDC system based on three control variables: pensions indexation, notional rate and contribution rate. The objective function considers both social adequacy and contribution rate sustainability, under liquidity and sustainability constraints. In the numerical application we apply the model to the Italian pension system and test the sensitivity of the results to different economic scenarios and objective function parameters.

Preparation and administration of medicaments body weight of animals and drug dosage

The body condition of a livestock is generally assessed by visual observation. The references to an animal being too thin, in good fl esh, or obese all relate to the animal’s weight. Therefore, the weight of an animal can be used as a measurement tool to determine its well-being, or the presence of problems which may threaten the health of the horse. The weight of small animalsand poultry may be carried out by balance by automatic balance machine several methods can be used to determine the body weight of livestock in an approximate scale.

Friction Influence on the Accuracy of the Rotors Automatic Balance

In the given paper the influence of friction forces in the bearing on the accuracy of automatic balancing unbalanced rotors by pendular automatic balance devices is considered. Magnitude of residual offset of a rotor–pendulums system depending on the friction forces is received, that allows defining residual vibration of the mechanism.