Continuous time model for notional defined contribution pension schemes: Liquidity and solvency

Abstract

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Mortality by socio-economic class and its impact on the retirement schemes: how to render the systems fairer?

“…In particular, our paper deals with two pay-as-you-go systems: a Defined Benefit (DB) and a Notional Defined Contribution (NDC) scheme. If in a DB scheme, the benefits are fixed based on the average salary and the contribution period of an individual, with the contribution rates deriving from the benefits 1 , in NDC schemes, each person has a notional account in which contributions are accumulated at a notional interest rate. At the retirement age, based on the mortality assumptions, the value accumulated into the accounts is transformed into a pension amount paid annually.…”

“…Moreover, mortality by socio-economic class is not considered in determining the benefits under the NDC systems, which generally make use of unisex mortality tables. To illustrate this point, we use projected salaries and mortality by level of education 3 to calculate and compare the DB or NDC pensions with the actuarially fair pensions (in other 1 DB schemes are widespread and countries such as Austria, France, Belgium, Spain, Japan and United States fall under this scheme [OCDE, [29]]. For a more detailed description of DB schemes, see Bodie et al [7] or Wilcox [47].…”

“…2 NDCs have been first implemented in Italy in 1995 and have since been introduced in countries such as Latvia (1996), Poland (1999), Sweden (1999) and Norway (2011). For a more detailed description of the NDC system, see, for example, Palmer [35], Börsch-Supan [8], Vidal-Meliá et al [45] or Arnold et al [2] and for a recent overview of country-specific features, see Alonso-García and Devolder [1]. 3 A list on the existing literature linking mortality to the level of education can be found in Ayuso et al [3].…”