Asymptotic Behavior of Central Order Statistics Under Monotone Normalization and Several Applications to Reinsurance

Latin America is facing the problems of ageing and the results of social security schemes (pensions) based on pay-as-you go basis or individual capitalization. In both cases, respectively problems are arising, due to the negative gap between incomes as contributions and expenditures, and on low replacement rates. My experience in actuarial valuations and pension reforms indicates that there is a need of sound actuarial participation, with elevated level of professionalism and applying ISAP-1 and ISAP-2, with high abilities in communication. Also, negotiation and transparency are important subjects. Different participants, like social and economic sectors, implies a complicate area to achieve an agreement. What actuaries can do? We must work in teams, without losing our identity and professionalism, combining quantitative activity with soft abilities, to obtain consensus and at least, to get a reasonable medium term interim solution. The paper will show guidelines to perform an appropriate work in this social conflictive area of actuarial practice.

Labor markets, typically subject to ageing population, today are sensible also to the implications still deriving from the recent Covid-19 pandemic. In such scenario, it is increasingly challenging to ensure that social security systems continue to meet their objectives of adequacy of benefits and sustainability constraints. Financial sustainability and adequacy of benefits are two sides of the same matter and must be jointly considered. In the medium to long term, unsustainable pension systems may not be able to guarantee enough level of the benefits. At the same time, the financial sustainability, pursued through a compression of the benefits, may be not socially feasible. In this work the so-called Pension Wealth indicator (PW) is used to measure the adequacy on benefits provided by social security schemes, in the light of the after effects of the pandemic with a focus on the Italian workers’ protection system. PW is the ratio between the actual value, on pensionable age, of all the pension payments that are expected to be paid (generally for the entire life) and the last salary received. PW is highly related to the future mortality trends and its study may give useful information on how to face the recent shocks on expectancy of life. PW can be thought as the lump-sum needed to buy an annuity giving the same cash flow as that of a generic annuity. The PW is generally referred to old age pensioners, but the aim of this study is to present a redefinition of PW with reference to specific vulnerable workers: the Italian injured worker broken down by accidents and occupational diseases and by impairment level.

What are the levers of attractiveness of long-term care insurance that we need to act on? In France, the creation of a 5th branch of Social Security dedicated to autonomy is a significant step forward. However public finances will not be able to assume the costs linked to the loss of autonomy of all our fellow citizens and families will not have all the financial resources to absorb the remaining expenses of their elders. These issues undeniably argue for the use of insurance solutions to support the public authorities. It is therefore essential that we, as actuaries, continue to work on making our long-term care products more desirable and durable. This workshop will be an opportunity to present an overview of the long-term care insurance market, highlighting in particular the issues, practices, market projects and prospects specific to this risk.