<abstract xmlns="http://www.w3.org/1999/xhtml">

The aim of this work is to provide the logical sustainability model for defined contribution pension systems (see [1], [2]) in the discrete framework under stochastic financial rate of the pension system fund and stochastic productivity of the active participants. In addition, the model is developed in the assumption of variable mortality tables.
Under these assumptions, the evolution equations of the fundamental state variables, the pension liability and the fund, are provided. In this very general discrete framework, the necessary and sufficient condition of the pension system sustainability, and all the other basic results of the logical sustainability theory, are proved.
In addition, in this work new results on the efficiency of the rule for the stabilization over time of the level of the unfunded pension liability with respect to wages, level that is defined as <italic>β</italic> indicator, are also proved.
</abstract>

The Logical Sustainability Theory for pension systems: the discrete-time model in a stochastic framework under variable mortality

<abstract xmlns="http://www.w3.org/1999/xhtml">

This paper adapts an actuarial mathematical model, built for the Italian public pension system, based on the law proposal 3035/2009 to the Accountant Pension Fund (CNPADC). The aim is to introduce a new philosophy pension highly correlated with the concept of adequacy for an ambitious social welfare; using the logic of the 3035/2009 proposal, which guarantees a minimum threshold for the replacement rate of the direct pension, this study provides a rigorous actuarial mathematical model that explains a sort of rate of contribution at a tendential equilibrium, in a pay-as-you-go pension system. This model reveals for which parameters it is possible to intervene to maintain the standard of living in retirement.
</abstract>

University of Naples Parthenope, DISAE University of Naples Parthenope

An actuarial mathematical model for a new pension philosophy. An application to the accountant pension fund

<abstract xmlns="http://www.w3.org/1999/xhtml">

The traditional criss-cross algorithm for the linear programming problem is shown to be finite when <bold>s</bold>-monotone index selection rules are used. The set of <bold>s</bold>-monotone index selection rules, among others, include the Last In First Out (LIFO) and the Most Often Selected Variable rule (MOSV). The advantage of applying the <bold>s</bold>-monotone index selection rule is the flexibility it provides in selecting the pivot element while still preserving the guarantee for finiteness. Such flexibility may be used to improve the numerical stability of the algorithm.
</abstract>

Finiteness of the criss-cross algorithm for the linear programming problem with s-monotone index selection rules

<abstract xmlns="http://www.w3.org/1999/xhtml">

Let <italic>G</italic> = <italic>G</italic>(<italic>n, m</italic>) be a rectangular solid grid graph and 𝒜(<italic>G</italic>) be a minimum length Eulerian augmentation of <italic>G</italic>. Let <italic>l</italic>0, . . ., <italic>lt</italic> ∈ ℕ such that ∑t<italic>i</italic>=0 <italic>li</italic> = <italic>|E</italic>(𝒜(<italic>G</italic>)<italic>|,</italic> where 2(<italic>n</italic> + <italic>m</italic>) <italic>≤ li</italic> = 2<italic>ki</italic>. In this paper, we exhibit a constructive procedure providing an edge-disjoint decomposition of 𝒜 (<italic>G</italic>) into closed trails <italic>T</italic>0, . . ., <italic>Tt</italic> such that <italic>|E</italic>(<italic>Ti</italic>)<italic>|</italic> = <italic>li</italic>.
</abstract>

Closed trail decompositions on grid graphs

AHEAD OF PRINT

Volume 30 (2022): Issue 4 (December 2022)

Volume 30 (2022): Issue 3 (October 2022) Special issue dedicated to 70th anniversary of prof. Peter Tallos

Volume 30 (2022): Issue 2 (August 2022)

Volume 30 (2022): Issue 1 (June 2022)

Volume 29 (2020): Issue 1 (December 2020)

Volume 28 (2019): Issue 1 (October 2019)

Volume 27 (2018): Issue 2 (August 2018)

Volume 27 (2018): Issue 1 (July 2018)

Volume 26 (2017): Issue 1 (June 2017)

Volume 25 (2015): Issue 2 (December 2015)

Volume 25 (2015): Issue 1 (September 2015)

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