In order to spread notional capital accrued at retirement by members of a cohort over their own life expectancy, pay-as-you-go notional-defined-contribution (payg-ndc) scheme uses multipliers (different by retirement age) called conversion coefficients. These are
backward-looking (b.l.) in that they relay on survival rates observed for previous cohorts in the past. Under increasing longevity, b.l. coefficients undervalue life expectancies, thus preventing full implementation of actuarial fairness (benefits equivalent to contributions) which is the
main objective of ndc scheme. They also engender chronic deficits.Forward-looking (f.l.) coefficients, relaying on forecast survival rates can improve actuarial fairness. Nevertheless, they face a rather serious political difficulty in that forecasting tools are fallible. This explains
why switching to f.l. coefficients is unable to gain social consensus. Apart from this, the paper shows that f.l. coefficients produce ‘overshooting’. In fact, they generate chronic surpluses. The paper also shows that frontloading pension profile helps sustainability because it
reduces both surpluses and deficits generated, respectively, by f.l. and b.l. coefficients.
In this paper we study the high frequency dynamic of financial volumes of traded stocks by using a semi-Markov approach. More precisely we assume that the intraday logarithmic change of volume is described by a weighted-indexed semi-Markov chain model. Based on this assumptions we show that this model is able to reproduce several empirical facts about volume evolution like time series dependence, intra-daily periodicity and volume asymmetry. Results have been obtained from a real data application to high frequency data from the Italian stock market from first of
Non-homogeneous renewal processes are not yet well established. One of the tools necessary for studying these processes is the non-homogeneous time convolution.\ud
Renewal theory has great relevance in general in economics and in particular in actuarial science, however most actuarial problems are connected with the age of the insured person. The introduction of non-homogeneity in the renewal processes brings actuarial applications closer to the real world. This paper will define the non-homogeneous time convolutions and try to give order to the non-homogeneous renewal processes. The numerical aspects of these processes are then dealt with and a real data application to an aspect of motorcar insurance is proposed
In this paper Markov models useful for following the time evolution of the aggregate claim amount and the claim number in the homogeneous time environment are presented. More precisely the homogeneous Markov reward processes in both discounted and not discounted cases are applied to solve the aggregate claim amount and the claim number processes respectively. In the last section the application of the proposed models is presented. Two different real-world databases are mixed for the construction of input data
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