A model for a programmed retirement pension scheme, with interest rates according to a continuous time Markov chain
The aim of this work is to study several aspects of the programmed retirement scheme, one of the three systems that currently conform the RAI or private saving pension system. For this purpose a stochastic model that describes the evolution of the individual account of a pensioner under this system, which allows one to answer a few key points about its performance. The model consists of a stochastic differential equation which is solved by the application of stochastic calculus with semimartingales. A basic component of the differential equation is a model for the fund returns, based on a nite Markov chain in continuous time. To implement this model parameters were estimated by maximum likelihood from a series of observed yields a portfolio of collective portfolios (duciaries). A modication of Euler's method for approximated solution of the equation, using simulated series of a finite Markov chain, in order to observe the dynamics of the reserves, was implemented. Based on these simulated results the distribution of the first passage time to an annuity for an annual minimum wage, as specied by Law, was estimated, as well as an estimate of the evolution of the payments made in the system. Some comments are in order, on the basis of two examples and the results obtained.
| Main Authors: | , |
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| Format: | Digital revista |
| Language: | spa |
| Published: |
Universidad Nacional de Colombia - Sede Medellín - Facultad de Ciencias
2014
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| Online Access: | https://revistas.unal.edu.co/index.php/rfc/article/view/50747 |
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