A multistage risk-averse stochastic programming model for personal savings accrual: the evidence from Lithuania
In this paper we consider the problem of choosing the optimal pension fund in the second pillar of Lithuanian pension system by providing some guidelines to individuals with defined contribution pension plans. A multistage risk-averse stochastic optimization model is proposed that can be used to plan a long-term pension accrual under two different cases: minimum and maximum accumulation plans as possible options in the system. The investment strategy of personal savings is based on the optimal solutions over possible scenario realizations generated for a particular participant. The concept of the risk-averse decision-maker is implemented by choosing the conditional value at risk as the risk measure defined by a nested formulation that guarantees the time consistency in the multistage model. The paper focuses on three important decision-making moments corresponding to the duration of periods to be modelled. The first period is a short-term accumulation, while the second period is a long-term accumulation with possibly high deviation of objective function value. The third period is designed to implement the concept of target date fund in the second pillar pension scheme as the subsequent need to protect against potential losses at risky pension funds. The experimental findings of this research provide insights for individuals as decision-makers to select pension funds, as well as for policy-makers by revealing the vulnerability of pension system.
KeywordsPension system modeling Multistage stochastic integer programming Alpha-stable distribution Time consistency CVaR Target date funds
Mathematics Subject Classification91B28 90C15 60E07 91B30
- Armonaite, G. (2012). Theoretical and practical aspects of assets and liabilities management in Lithuanian pension funds. http://archive.ism.lt/handle/1/263. Accessed June 01, 2016.
- Bank of Lithuania. (2013). Reviews of Lithuania’s 2nd and 3rd pillar pension funds and of the market of collective investment undertakings. https://www.lb.lt/en/publications/review-of-lithuania-s-2nd-and-3rd-pillar-pension-funds-and-of-the-market-of-collective-investment-undertakings-2013. Accessed May 26, 2016.
- Bank of Lithuania. (2014). Reviews of Lithuania’s 2nd and 3rd pillar pension funds and of the market of collective investment undertakings. https://www.lb.lt/en/publications/reviews-of-lithuania-s-2nd-and-3rd-pillar-pension-funds-and-of-the-market-of-collective-investment-undertakings-2014. Accessed May 26, 2016.
- Bank of Lithuania. (2015). Reviews of Lithuania’s 2nd and 3rd pillar pension funds and of the market of collective investment undertakings. https://www.lb.lt/en/publications/review-of-lithuania-s-2nd-and-3rd-pillar-pension-funds-and-of-the-market-of-collective-investment-undertakings-2015. Accessed May 26, 2016.
- Bitinas, A. (2011). Modern pension system reforms in Lithuania: Impact of crisis and ageing. Jurispridencija, 18(3), 1055–1080.Google Scholar
- Bitinas, A., & Maccioni, A. (2013). Lithuanian pension systems reforms following demographic and social transitions. http://crenos.unica.it/crenos/sites/default/files/WP13-15_0.pdf. Accessed June 01, 2016.
- Bitinas, A., & Maccioni, A. (2014). Lithuanian pension system’s reforms transformations and forecasts. Universal Journal of Industrial and Business Management, 2(1), 13–23.Google Scholar
- Chybalski, F. (2015). The choice of open pension fund made by citizens of Poland in the year 2003–2009: The analysis of the criteria. https://www.econbiz.de/Record/the-choice-of-open-pension-fund-made-by-citizens-of-poland-in-the-years-2003-2009-the-analysis-of-the-criteria-chybalski-filip/10008904670. Accessed 05 June, 2016.
- Cobbe, H. (2014). Target date funds: Will the UK follow the American Revolution. Professional Investor (October 2014). Journal of the CFA Society of the UK. Elston Research Series. https://view.joomag.com/elston-research-series/0172454001413204307
- Gavrilova, I. (2011). The evaluation of mutual fund performance in Lithuania considering risk and timing ability. Business in XXI Century, 3(4), 5–12.Google Scholar
- Goldfeld, S., & Quantd, R. (2005). A Markov model for switching regression. Journal of Econometrics, 135, 349–376.Google Scholar
- Gudaitis, T., & Maccioni, A. F. (2014). Optimal individual choice of contribution to second pillar pension system in Lithuania. https://ideas.repec.org/p/cns/cnscwp/201402.html. Accessed May 23, 2016.
- Gudaitis, T., & Medaiskis, T. (2013). Was the participation in second pillar successful in Lithuania? In Atiner’s conference paper series Athens. Athens Institute for Education and Research.Google Scholar
- Hammond, B. (2015). Target date funds: The good, the bad, and the unknown. Forbes (June 2015). Forbes Media LLC. https://www.forbes.com/sites/pensionresearchcouncil/2015/07/29/target-date-funds-the-good-the-bad-and-the-unknown/#3c93c2fa400a
- Jurevičiene, D., & Samoškaite, Š. (2012). Evaluation of pillar II pension funds return on investment considering risk. Business: Theory and Practice, 13(4), 304–313.Google Scholar
- Kabašinskas, A., Rachev, S., Sakalauskas, L., Sun, W., & Belovas, I. (2010). Stable mixture model with dependent states for financial return series exhibiting short histories and periods of strong passivity. Computational Analysis and Applications, 12(1), 268–292.Google Scholar
- Kabašinskas, A., Sakalauskas, L., Sun, W., & Belovas, I. (2012). Mixed-stable models for analyzing high-frequency financial data. Journal of Computational Analysis and Applications, 14(7), 1210–1226.Google Scholar
- Kaut, M., & Wallace, S. W. (2007). Evaluation of scenario-generation methods for stochastic programming. Pacific Journal of Optimization, 3, 257–271.Google Scholar
- Liutvinavičius, M., & Sakalauskas, V. (2011). Research of factors affecting pension funds efficiency. Social Technologies, 1(2), 328–343.Google Scholar
- Medaiskis, T., & Gudaitis, T. (2013). Assessing the impact of second pillar component on old age pension in Lithuania. Ekonomika, 92(4), 54–72.Google Scholar
- Medaiskis, T., & Jankauskiene, D. (2014). Pensions, health and long-term care. Lithuania. http://ec.europa.eu/social/BlobServlet?docId=12972&langId=en. Accessed June 02, 2016.
- Mladen, L. (2012). A comparative review over the pension systems performance in Central and Eastern European countries. Journal of Knowledge Management, Economics and Information Technology, 5, 11.Google Scholar
- OECD. (2013). Pensions at a glance 2013: OECD and g20 indicators. http://www.oecd.org/pensions/public-pensions/OECDPensionsAtAGlance2013.pdf. Accessed May 24, 2016.
- Pension Funds Online. (2016). Lithuania. http://www.pensionfundsonline.co.uk/content/country-profiles/lithuania/87. Accessed May 23, 2016.
- Samorodnitsky, G., & Taqqu, M. (2000). Stable non-Gaussian random processes, stochastic models with infinite variance. New York: Chapman & Hall.Google Scholar
- Seimas of the Republic of Lithuania. (2010). Law on reform of the pension system. http://www3.lrs.lt/pls/inter3/dokpaieska.showdoc_e?p_id=382018&p_tr2=2, reg. num. IX-1215.
- Skučiene, D. (2011). Kaupiamuju pensiju schemos dalyviu elgsenos tendencijos lietuvoje. Filosofija Sociologija, 22(2), 226–235.Google Scholar
- Šutiene, K., Kabašinskas, A., Strebeika, D., Kopa, M., & Reichardt, R. (2014). Estimation of VaR and CVaR from financial data using simulated alpha-stable random variables. In Proceedings of the 28th European simulation and modelling conference, FEUP, University of Porto, Porto, Portugal.Google Scholar
- Šutiene, K., Makackas, A., & Pranevicius, H. (2010). Multistage k-means clustering for scenario tree construction. Informatica, 21(1), 123–138.Google Scholar
- Velculescu, D. (2011). Pension reforms in emerging Europe: The uncertain road ahead. http://www.ebrd.com/downloads/research/news/4441347_-_Pension_Reforms_in_Emerging_Europe_The_Uncertain_Road_Ahead_(D.Velculescu)_-_1_-_DMSDR1S.pdf. Accessed June 02, 2016.
- Volskis, E. (2012). Reforms of Baltic states pension systems: Challenges and benefits. http://www.ebrd.com/downloads/news/pension-system.pdf. Accessed June 02, 2016.
- Zochowski, D., & Bialowolski, P. (2011). Modelling inflation using Markov switching models: Case of Poland. Prace i Materiay, 86, 185–199.Google Scholar