Dynamic stochastic accumulation model with application to pension savings management
DOI:
https://doi.org/10.2298/YJOR1001001MKeywords:
dynamic stochastic programming, funded pillar, utility function, Bellman equation, Slovak pension system, risk aversion, pension portfolio simulationsAbstract
We propose a dynamic stochastic accumulation model for determining optimal decision between stock and bond investments during accumulation of pension savings. Stock prices are assumed to be driven by the geometric Brownian motion. Interest rates are modeled by means of the Cox-Ingersoll-Ross model. The optimal decision as a solution to the corresponding dynamic stochastic program is a function of the duration of saving, the level of savings and the short rate. Qualitative and quantitative properties of the optimal solution are analyzed. The model is tested on the funded pillar of the Slovak pension system. The results are calculated for various risk preferences of a saver.References
Aaron, H. (1966) 'The social security paradox. Canadian Journal of Economics and Political Science, 32(3): 371
Bergstrom, A.R. (1983) Gaussian estimation of structural parameters in higher order continuous time dynamic models. Econometrica, 51(1): 117
Bodie, Z. (1999) Investment, management and technology: Past, present and future. u: Brookings-Wharton papers on financial services, Washington, DC: Brookings Institution Press
Bodie, Z., Detemple, J.B., Otruba, S., Walter, S. (2003) Optimal consumption-portfolio choices and retirement planning. Journal of Economic Dynamics & Control, 28, 1115-1148
Bodie, Z., Merton, R.C., Samuelson, W. (1992) Labor supply flexibility and portfolio choice in a life-cycle model. Journal of Economic Dynamics and Control, vol. 16: 427-449
Bodie, Z. (1995) On the risk of stocks in the long run. Financial Analysts Journal, May-Jun: 18-22
Cox, J., Ingersoll, J., Ross, S. (1985) A theory of the term structure of interest rates. Econometrica, 53(2): 385
Friend, I., Blume, M.E. (1975) The demand for risky sssets. American Economic Review, 65 900-922
Hull, J. (1989) Options, futures, and other derivative securities. London: Prentice-Hall International
Jamshidian, F. (1997) LIBOR and Swap Market Models and Measures. Finance and Stochastics, 1(4): 293
Jamshidian, F. (1988) The one-factor Gaussian interest rate model: Theory and implementation. Working paper, Merril Lynch Capital Markets
Kilianová, S. (2006) The second pillar of the Slovak pension system: Interest rate targeting. Journal of Electrical Engineering, 57 51-54
Kilianová, S., Melicherčík, I., Ševčovič, D. (2006) Dynamic accumulation model for the second pillar of the Slovak pension system. Czech Journal for Economics and Finance, 11-12, 506-521
Kilianová, S., Pflug, G. (2009) Optimal pension fund management under multi-period risk minimization. Ann. Oper. Res., 166: 261
Kvetan, V., Mlýnek, M., Páleník, V., Radvanský, M. (2007) Starnutie, zdravotný stav a determinanty výdavkov na zdravie v podmienkach Slovenska. Bratislava: Research studies of Institute of Economics
Kwok, Y.K. (1998) Mathematical models of financial derivatives. New York - Heidelberg - Berlin: Springer
Markowitz, H.M. (1952) Portfolio selection. Journal of Finance, vol. 7, mart, str. 77-91
Medved', M. (1992) Fundamentals of dynamical systems and bifurcation theory. Bristol: Adam Hilger
Mehra, R., Prescott, E. (1985) The equity premium: A puzzle. Journal of Monetary Economics, 15(2): 145
Melicherčík, I., Ungvarský, C. (2004) Pension reform in Slovakia: Perspectives of the fiscal debt and pension level. Czech Journal for Economics and Finance, 9-10, 391-404
Merton, R.C., Samuelson, P.A. (1974) Fallacy of the log-normal approximation to optimal portfolio decision-making over many periods. Journal of Financial Economics, 1(1): 67
Merton, R.C. (1975) Theory of finance from the perspective of continuous time. Journal of Financial and Quantitative Analysis, 10(4): 659
Merton, R.C. (1992) Continuous-time finance. Oxford, UK, itd: Blackwell
Merton, R.C. (1971) Optimum consumption and portfolio rules in a continuous-time model. Journal of Economic Theory, 3, Dec: 373-413
Merton, R.K. (1969) Lifetime portfolio selection under uncertainty: The continuous-time case. Review of Economics and Statistics, vol. 51, avgust, str. 247-257
Mitková, V., Mlynarovič, V., Tuš, B. (2007) A performance and risk analysis on the slovak private pension funds market. Ekonomický časopis, 55, 232-249
Nowman, K.B. (1997) Gaussian estimation of single-factor continuous time models of the term structure of interest rates. Journal of Finance, 52(4): 1695
Orszag, P.R., Stiglitz, J.E. (1999) Rethinking pension reform: ten myths about social security system. u: conference on New Ideas about Old Age Security, Washington: World Bank, 14-15
Pratt, J. (1964) Risk aversion in the small and in the large. Econometrica, 32, 2, 122-136
Rebonato, R. (1998) Interest-rate options model. New York: John Willey & Sons Inc
Samuelson, P.A. (1969) Lifetime portfolio selection by dynamic stochastic programming. Review of Economics and Statistics, 51, str. 239-246
Ševčovič, D., Urbánová, C.A. (2005) On a two-phase minmax method for parameter estimation of the Cox, Ingersoll, and Ross interest rate model. Central European Journal of Operational Research, 13 169-188
Tobin, J. (1958) Liquidity preference as behavior towards risks. Review of Economic Studies, vol. 25, februar, str. 68-85
Young, H.P. (1990) Progressive taxation and equal sacrifice. American Economic Review, 80, str. 253-266
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