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Stochastic model of a pension plan


  • Paz Grimberg
  • Zeev Schuss


Structuring a viable pension plan is a problem that arises in the study of financial contracts pricing and bears special importance these days. Deterministic pension models often rely on projections that are based on several assumptions concerning the "average" long-time behavior of the stock market. Our aim here is to examine some of the popular "average" assumptions in a more realistic setting of a stochastic model. Thus, we examine the contention that investment in the stock market is similar to gambling in a casino, while purchasing companies, after due diligence, is safer under the premise that acting as a holding company that wholly owns other companies avoids some of the stock market risks. We show that the stock market index faithfully reflects its companies' profits at the time of their publication. We compare the shifted historical dynamics of the S\&P500's aggregated financial earnings to its value, and find a high degree of correlation. We conclude that there is no benefit to a pension fund in wholly owning a super trust. We verify, by examining historical data, that stock earnings follow an exponential (geometric) Brownian motion and estimate its parameters. The robustness of this model is examined by an estimate of a pensioner's accumulated assets over a saving period. We also estimate the survival probability and mean survival time of the accumulated individual fund with pension consumption over the residual life of the pensioner.

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  • Paz Grimberg & Zeev Schuss, 2014. "Stochastic model of a pension plan," Papers 1407.0517,
  • Handle: RePEc:arx:papers:1407.0517

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    1. Muhammad, Shahbaz & Muhammad, Nasir Malik & Muhammad, Shahbaz Shabbir, 2011. "Does economic growth cause terrorism in Pakistan?," MPRA Paper 35101, University Library of Munich, Germany, revised 30 Nov 2011.
    2. Uri Gneezy & Teck-Hua Ho & John List, 2011. "Editorial Statement: Behavioral Economics," Management Science, INFORMS, vol. 57(7), pages 1-1, July.
    3. Haskel, Jonathan & Wallis, Gavin, 2013. "Public support for innovation, intangible investment and productivity growth in the UK market sector," Economics Letters, Elsevier, vol. 119(2), pages 195-198.
    4. Justin Yifu Lin, 2011. "China and the global economy," Proceedings, Federal Reserve Bank of San Francisco, issue Nov, pages 213-229.
    5. Liparã Daniel, 2011. "Why Is Human Capital a Driver for Economic Growth?," Ovidius University Annals, Economic Sciences Series, Ovidius University of Constantza, Faculty of Economic Sciences, vol. 0(1), pages 1160-1165, May.
    6. Sungbae An & Heedon Kang, 2011. "Oil Shocks in a DSGE Model for the Korean Economy," NBER Chapters, in: Commodity Prices and Markets, pages 295-321, National Bureau of Economic Research, Inc.
    7. Tin-Chun Lin, 2011. "Economic effects of grades on course evaluations," Applied Economics Letters, Taylor & Francis Journals, vol. 18(12), pages 1195-1199.
    8. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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