Entrance times of random walks: With applications to pension fund modeling

Jarner, Søren Fiig; Kronborg, Morten Tolver

doi:10.1016/j.insmatheco.2015.11.006

Cited by 3 publications

(1 citation statement)

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“…After the presentation of "Materials and Methods", the "Gambler's Ruin Probability" is calculated, and the "Fund Ruin Probability" is studied. Then follows a "Ruin Probability's Particularization" using normal distributions, and the characterization of Assets and Liability Management Politics through a generalized Brownian motion process, see Ferreira and Filipe [12] and Jarner and Kronborg [13]. Follow the "Discussion", and the "Conclusions".…”

Section: Introductionmentioning

confidence: 99%

Addressing Reserves and Pension Funds through Gambler’s Ruin and Generalized Brownian Motion Process

Ferreira

Filipe

2021

Recent Advances in Mathematical Research and Computer Science Vol. 4

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We used the random walk to model the problem of reserves. The classic case of a stochastic process is the example of random walks, which are used to study a set of phenomena and, particularly, as in this article, to study models of reserves evolution. Random walks also allow the construction of significant complex systems and are used as an instrument of analysis, being used in this study for giving a theoretical characteristic to specific types of systems. Our goal is mainly to study reserves to see how to ensure that pension funds are sustainable. This paper, by covering a classic approach to the study of pension funds, makes possible to draw interesting conclusions about the problem of reserves. We also consider the Brownian motion to model the pensions fund assets and liability management politics. In this context, it was possible to obtain expressions for the expected value of the pensions fund perpetual maintenance cost present value, also for the expected value of the maintenance cost up to time t, indicators of a fund maintenance policy expenditures.

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Section: Introductionmentioning

confidence: 99%

Addressing Reserves and Pension Funds through Gambler’s Ruin and Generalized Brownian Motion Process

Ferreira

Filipe

2021

Recent Advances in Mathematical Research and Computer Science Vol. 4

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Pension system design: roles and interdependencies of tax-financed and funded pensions

Jarner,

Jallbjørn,

Andersen

2024

Scandinavian Actuarial Journal

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First Passage Analysis in a Queue with State Dependent Vacations

Dshalalow

White

2022

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This paper deals with a single-server queue where the server goes on maintenance when the queue is exhausted. Initially, the maintenance time is fixed by deterministic or random number T. However, during server’s absence, customers are screened by a dispatcher who estimates his service times based on his needs. According to these estimates, the dispatcher shortens server’s maintenance time and as the result the server returns earlier than planned. Upon server’s return, if there are not enough customers waiting (under the N-Policy), the server rests and then resumes his service. At first, the input and service are general. We then prove a necessary and sufficient condition for a simple linear dependence between server’s absence time (including his rest) and the number of waiting customers. It turns out that the input must be (marked) Poisson. We use fluctuation and semi-regenerative analyses (previously established and embellished in our past work) to obtain explicit formulas for server’s return time and the queue length, both with discrete and continuous time parameter. We then dedicate an entire section to related control problems including the determination of the optimal T-value. We also support our tractable formulas with many numerical examples and validate our results by simulation.

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Entrance times of random walks: With applications to pension fund modeling

Cited by 3 publications

References 32 publications

Addressing Reserves and Pension Funds through Gambler’s Ruin and Generalized Brownian Motion Process

Addressing Reserves and Pension Funds through Gambler’s Ruin and Generalized Brownian Motion Process

Pension system design: roles and interdependencies of tax-financed and funded pensions

First Passage Analysis in a Queue with State Dependent Vacations

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