Optimal mix among PAYGO, EET and individual savings

References

• Aaron, H. J. (1966). The social insurance paradox. Canadian Journal of Economics and Political Science 32, 371–374.
   Google Scholar
• Beetsma, R. M. W. J. & Bovenberg, A. L. (2009). Pensions and intergenerational risk sharing in general equilibrium. Economica 76, 364–386.
   Web of Science ®Google Scholar
• Beetsma, R. M. W. J., Romp, W. E. & Vos, S. J. (2012). Voluntary participation and intergenerational risk sharing in a funded pension system. European Economic Review 56, 1310–1324.
   Web of Science ®Google Scholar
• Benzoni, L., Collin-Dufresne, P. & Goldstein, R. S. (2007). Portfolio choice over the life-cycle when the stock and labor markets are cointegrated. The Journal of Finance 62(5), 2123–2167.
   Web of Science ®Google Scholar
• Beshears, J., Choi, J. J., Laibson, D. & Madrian, B. C. (2017). Does front-loading taxation increase savings? Evidence from Roth 401(K) introductions. Journal of Public Economics 151, 84–95.
   PubMed Web of Science ®Google Scholar
• Bodie, Z., Detemple, J. B., Otruba, S. & Walter, S. (2004). Optimal consumption-portfolio choices and retirement planning. Journal of Economic Dynamics and Control 28, 1115–1148.
   Web of Science ®Google Scholar
• Chen, A., Hentschel, F. & Xu, X. (2018). Optimal retirement time under habit persistence: what makes individuals retire early?. Scandinavian Actuarial Journal 2018, 225–249.
   Web of Science ®Google Scholar
• Cui, J., de Jong, F. & Ponds, E. (2011). Intergenerational risk sharing within funded pension schemes. Journal of Pension Economics and Finance 10, 1–29.
   Web of Science ®Google Scholar
• De Menil, G., Murtin, F. & Sheshinski, E. (2006). Planning for the optimal mix of paygo tax and funded savings. Journal of Pension Economics and Finance 5, 1–25.
   Google Scholar
• Devolder, P. & Melis, R. (2015). Optimal mix between pay as you go and funding for pension liabilities in a stochastic framework. ASTIN Bulletin 45, 551–575.
   Web of Science ®Google Scholar
• Dickson, D. C., Hardy, M. R. & Waters, H. R. (2013). Actuarial mathematics for life contingent risks. Cambridge University Press.
   Google Scholar
• Dutta, J., Kapur, S. & Orszag, J. M. (2000). A portfolio approach to the optimal funding of pensions. Economic Letters 69, 201–206.
   Web of Science ®Google Scholar
• Fu, K., Rong, X. & Zhao, H. (2023). Optimal investment problem for a hybrid pension with intergenerational risk-sharing and longevity trend under model uncertainty. arXiv preprint arXiv:2302.02351.
   Google Scholar
• Guigou, J. D., Lovat, B. & Schiltz, J. (2012). Optimal mix of funded and unfunded pension systems: the case of Luxembourg. Pensions 17, 208–222.
   Google Scholar
• Hansson, I. & Stuart, C. (1989). Social security as trade among living generations. American Economic Review 79, 1182–1195.
   Web of Science ®Google Scholar
• Hassler, J. & Lindbeck, A. (1997). Optimal actuarial fairness in pension systems: a note. Economic Letters55, 251–255.
   Web of Science ®Google Scholar
• He, L., Liang, Z. X., Song, Y. L. & Ye, Q. (2021). Optimal contribution rate of PAYGO pension. Scandinavian Actuarial Journal 2021, 505–531.
   Web of Science ®Google Scholar
• Hirsch, C. (1988). Numerical computation of internal & external flows: fundamentals of numerical discretization. New York: John Wiley & Sons, Inc.
   Google Scholar
• In't Hout, K. J. & Welfert, B. D. (2007). Stability of ADI schemes applied to convection-diffusion equations with mixed derivative terms. Applied Numerical Mathematics 57(1), 19–35.
   Web of Science ®Google Scholar
• Jin, F. (2020). Life-cycle portfolio choice with a realistic retirement age distribution. Available at SSRN: DOI: 10.2139/ssrn.1098166
   Google Scholar
• Marimon, R. & Scott, A. (1999). Computational methods for the study of dynamic economies. Oxford: Oxford University Press.
   Google Scholar
• Meijdam, L. & Verbon, H. A. A. (1996). Aging and political decision making on public pensions. Journal of Population Economics 9, 141–158.
   PubMed Web of Science ®Google Scholar
• Merton, R. C. (1969). Lifetime portfolio selection under uncertainty: the continuous-time case. The Review of Economics and Statistics 51, 247–257.
   Web of Science ®Google Scholar
• Merton, R. C. (1983). On the role of social security as a means for efficient risk sharing in an economy where human capital is not tradeable. In Bodie, Z., Shoven, J. B.(Eds.), Financial aspects of the United States pension system. Chicago, IL: The University of Chicago Press. P. 325–358.
   Google Scholar
• Nash, J. F. (1950). The bargaining problem. Econometrica 18, 155–162.
   Web of Science ®Google Scholar
• Samuelson, P. A. (1958). An exact consumption-loan model of interest with or without the social contrivance of money. Journal of Political Economy 66, 467–482.
   Web of Science ®Google Scholar
• Selten, R. (1965). Spieltheoretische behandlung eines oligopolmodells mit nachfrageträgheit: teil i: bestimmung des dynamischen preisgleichgewichts. Zeitschrift Für Die Gesamte Staatswissenschaft/Journal of Institutional and Theoretical Economics, (H. 2) 121, 301–324.
   Google Scholar
• Van Praag, B. M. & Cardoso, P.(2003). The mix between pay-as-you-go and funded pensions and what demography has to do with it. Available at SSRN 385106.
   Google Scholar
• Wang, S. X., Lu, Y. & Sanders, B. (2018). Optimal investment strategies and intergenerational risk sharing for target benefit pension plans. Insurance: Mathematics and Economics 80, 1–14.
   Web of Science ®Google Scholar
• Yong, J. & Zhou, X. Y. (1999). Stochastic controls: Hamiltonian systems and HJB equations. New York: Springer Science Business Media.
   Google Scholar