Abstract
In this paper we recall and summarize results on a dynamic stochastic accumulation model for determining optimal decision between stock and bond investments during accumulation of pension savings. We assume stock prices to be driven by a geometric Brownian motion whereas interest rates are modeled by means of a one factor interest rate model. It turns out that the optimal decision representing stock to bond proportion is a function of the duration of saving, the level of savings and the short rate. We furthermore summarize the results of testing the model on the fully funded second pillar of the Slovak pension system.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Battochio, P.& Menoncin, F.: Optimal pension management in a stochastic framework, Insur.: Math. & Econ. 34, 79–95 (2004)
Bodie, Z., Merton, R. & Samuelson, W.F.: Labor supply flexibility and portfolio choice in a life-cycle model, J. of Econ. Dyn. & Control 16, 427–449 (1992)
Cairns, A., Blake, D. & Dowd, K.: Stochastic lifestyling: Optimal dynamic asset allocation for defined contribution pension plans, J. of Econ. Dyn. & Control 30, 843–877 (2006)
Deelstra, G., Grasselli, M. & Koehl, P.: Optimal investment strategies in a CIR framework, J. of Appl. Prob. 37, 936–946 (2000)
Kilianová, S., Melicherčík, I. & Ševčovič, D.: Dynamic accumulation model for the second pillar of the Slovak pension system, Czech J. of Econ. and Finance 11–12, 506–521 (2006)
Kvetan, V., Mlýnek, M., Páleník, V. & Radvanský, M.: Starnutie, zdravotný stav a determinant výdavkov na zdravie v podmienkach Slovenska. Research studies of Institute of Economics SAV, Bratislava (2007)
Ma, Q.P.: On ”optimal pension management in a stochastic framework” with exponential utility, Insur.: Math. & Econ. 49, 61–69 (2011)
Melicherčík, I. & Ševčovič, D.: Dynamic stochastic accumulation model with application to pension savings management, Yugoslav J. of Oper. Res. 20, 1–24 (2010)
Merton, R.C. & Samuelson, P.A.: Fallacy of the log-normal approximation to optimal portfolio decision-making over many periods, J. of Finan. Econ. 1, 67–94 (1974)
Milevsky, M.: Optimal asset allocation towards the end of the life cycle: to annuitize or not to annuitize? J. of Risk and Insur. 65, 401–426 (1998)
Samuelson, P.A.: Lifetime portfolio selection by dynamic stochastic programming, The Rev. of Econ. and Stat. 51, 239–246 (1969)
Ševčovič, D. & Urbánová Csajková, A.: On a two-phase minmax method for parameter estimation of the Cox, Ingersoll, and Ross interest rate model. Central Eur. J. of Oper. Res. 13, 169–188 (2005)
Acknowledgements
This work has been supported by ERDF-017/2009/4.1/OPVaV-CESIUK and VEGA 1/0381/09 projects.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Italia
About this chapter
Cite this chapter
Melicherčík, I., Ševčovič, D. (2012). Dynamic model of pension savings management with stochastic interest rates and stock returns. In: Perna, C., Sibillo, M. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance. Springer, Milano. https://doi.org/10.1007/978-88-470-2342-0_35
Download citation
DOI: https://doi.org/10.1007/978-88-470-2342-0_35
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-2341-3
Online ISBN: 978-88-470-2342-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)