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

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.

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