Equilibrium and Maintenance Costs of Pensions Funds Studied through Stochastic Processes | Chapter 7 | Mathematics and Computer Science: Contemporary Developments Vol. 9

In this study, a representation is depicted of a pension fund through a stochastic network with two infinite servers’ nodes. With this representation, it is allowed to deduce an equilibrium condition of the system with a basis on the identity of the random rates expected values, for which the contributions arrive at the fund and the pensions are paid by the fund. Then, to address situations of imbalance, the generic case of a pension fund that is not sufficiently auto-financed, and is thoroughly maintained with an external financing effort is considered in this chapter. To represent the unrestricted reserves value process of this kind of fund, a time-homogeneous diffusion stochastic process with finite expected time to ruin is proposed. Then it is projected a financial tool that regenerates the diffusion at some level with a positive value every time the diffusion hits a barrier placed at the origin. So, the financing effort can be modeled as a renewal-reward process if the regeneration level is preserved constantly. The perpetual maintenance cost expected values and the finite-time maintenance cost evaluations are studied. An application of this approach when the unrestricted reserves value process behaves as a generalized Brownian motion process is presented.

 

Author (s) Details

 

Manuel Alberto M. Ferreira
Department of Mathematics, ISTA—School of Technology and Architecture, Iscte – Lisbon University Institute. Information Sciences, Technologies and Architecture Research Center (ISTAR-IUL), 1649-026 Lisbon, Portugal.

 

Please see the book here:- https://doi.org/10.9734/bpi/mcscd/v9/3369

Addressing Reserves and Pension Funds through Gambler’s Ruin and Generalized Brownian Motion Process | Chapter 2 | Recent Advances in Mathematical Research and Computer Science Vol. 4

 The random walk was used to model the reserve problem. Random walks are a classic example of a stochastic process that can be used to examine a variety of phenomena, including, as in this article, models of reserve evolution. Random walks can also be used to build major complicated systems and as an analytical tool; they were utilised in this study to give specific sorts of systems a theoretical characteristic. Our main purpose is to investigate reserves in order to determine how to keep pension funds afloat. This work, by addressing a traditional approach to the research of pension funds, allows for some intriguing conclusions to be drawn concerning the reserve problem. We also use the Brownian motion to describe the assets and liability management politics of pension funds. In this context, expressions for the expected value of the pensions fund perpetual maintenance cost present value, as well as the expected value of the maintenance cost up to time t, were obtained, as well as indications of a fund's maintenance policy expenditures.

Author(S) Details

Manuel Alberto M. Ferreira
Department of Mathematics, ISTA—School of Technology and Architecture, ISCTE - Instituto Universitário de Lisboa, Information Sciences, Technologies and Architecture Research Center (ISTAR-IUL), Business Research Unit-IUL (BRU-IUL), 1649-026 Lisbon, Portugal.

José António Filipe
Department of Mathematics, ISTA—School of Technology and Architecture, ISCTE - Instituto Universitário de Lisboa, Information Sciences, Technologies and Architecture Research Center (ISTAR-IUL), Business Research Unit-IUL (BRU-IUL), 1649-026 Lisbon, Portugal.

View Book:- https://stm.bookpi.org/RAMRCS-V4/article/view/4868