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Pension funds with a minimum guarantee: a stochastic control approach

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  • Marina Di Giacinto
  • Salvatore Federico
  • Fausto Gozzi

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  • Marina Di Giacinto & Salvatore Federico & Fausto Gozzi, 2011. "Pension funds with a minimum guarantee: a stochastic control approach," Finance and Stochastics, Springer, vol. 15(2), pages 297-342, June.
    • Handle: RePEc:spr:finsto:v:15:y:2011:i:2:p:297-342
    DOI: 10.1007/s00780-010-0127-7
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    References listed on IDEAS

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    1. Deelstra, Griselda & Grasselli, Martino & Koehl, Pierre-Francois, 2003. "Optimal investment strategies in the presence of a minimum guarantee," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 189-207, August.
    2. Deelstra, Griselda & Grasselli, Martino & Koehl, Pierre-Francois, 2004. "Optimal design of the guarantee for defined contribution funds," Journal of Economic Dynamics and Control, Elsevier, vol. 28(11), pages 2239-2260, October.
    3. Nicole El Karoui & Asma Meziou, 2008. "Max-Plus decomposition of supermartingales and convex order. Application to American options and portfolio insurance," Papers 0804.2561, arXiv.org.
    4. Blanchet-Scalliet, Christophette & El Karoui, Nicole & Jeanblanc, Monique & Martellini, Lionel, 2008. "Optimal investment decisions when time-horizon is uncertain," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1100-1113, December.
    5. Paolo Battocchio & Francesco Menoncin & Olivier Scaillet, 2007. "Optimal asset allocation for pension funds under mortality risk during the accumulation and decumulation phases," Annals of Operations Research, Springer, vol. 152(1), pages 141-165, July.
    6. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin, 2006. "Stochastic lifestyling: Optimal dynamic asset allocation for defined contribution pension plans," Journal of Economic Dynamics and Control, Elsevier, vol. 30(5), pages 843-877, May.
    7. Goldys, B. & Gozzi, F., 2006. "Second order parabolic Hamilton-Jacobi-Bellman equations in Hilbert spaces and stochastic control: approach," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1932-1963, December.
    8. Sethi, Suresh P. & Taksar, Michael I. & Presman, Ernst L., 1992. "Explicit solution of a general consumption/portfolio problem with subsistence consumption and bankruptcy," Journal of Economic Dynamics and Control, Elsevier, vol. 16(3-4), pages 747-768.
    9. A. Cadenillas & S. P. Sethi, 1997. "Consumption-Investment Problem with Subsistence Consumption, Bankruptcy, and Random Market Coefficients," Journal of Optimization Theory and Applications, Springer, vol. 93(2), pages 243-272, May.
    10. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    11. Ioannis Karatzas & John P. Lehoczky & Suresh P. Sethi & Steven E. Shreve, 1986. "Explicit Solution of a General Consumption/Investment Problem," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 261-294, May.
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    13. Griselda Deelstra & Martino Grasselli & Pierre-François Koehl, 2003. "Optimal investment strategies in the presence of a minimum guarantee," ULB Institutional Repository 2013/7598, ULB -- Universite Libre de Bruxelles.
    14. Salvatore Federico, 2011. "A stochastic control problem with delay arising in a pension fund model," Finance and Stochastics, Springer, vol. 15(3), pages 421-459, September.
    15. Steven Haberman & Elena Vigna, 2002. "Optimal investment strategies and risk measures in defined contribution pension schemes," ICER Working Papers - Applied Mathematics Series 09-2002, ICER - International Centre for Economic Research.
    16. Haberman, Steven & Vigna, Elena, 2002. "Optimal investment strategies and risk measures in defined contribution pension schemes," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 35-69, August.
    17. Schwartz, Eduardo S & Tebaldi, Claudio, 2004. "Illiquid Assets and Optimal Portfolio Choice," University of California at Los Angeles, Anderson Graduate School of Management qt7q65t12x, Anderson Graduate School of Management, UCLA.
    18. Bruno Bouchard & Huyên Pham, 2004. "Wealth-path dependent utility maximization in incomplete markets," Finance and Stochastics, Springer, vol. 8(4), pages 579-603, November.
    19. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    20. repec:dau:papers:123456789/1803 is not listed on IDEAS
    21. El Karoui, Nicole & Jeanblanc, Monique & Lacoste, Vincent, 2005. "Optimal portfolio management with American capital guarantee," Journal of Economic Dynamics and Control, Elsevier, vol. 29(3), pages 449-468, March.
    22. Starks, Laura T., 1987. "Performance Incentive Fees: An Agency Theoretic Approach," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(1), pages 17-32, March.
    23. Vigna, Elena & Haberman, Steven, 2001. "Optimal investment strategy for defined contribution pension schemes," Insurance: Mathematics and Economics, Elsevier, vol. 28(2), pages 233-262, April.
    24. Griselda Deelstra & Martino Grasselli & Pierre-François Koehl, 2004. "Optimal design of the guarantee for defined contribution funds," ULB Institutional Repository 2013/7602, ULB -- Universite Libre de Bruxelles.
    25. Duffie, Darrell & Fleming, Wendell & Soner, H. Mete & Zariphopoulou, Thaleia, 1997. "Hedging in incomplete markets with HARA utility," Journal of Economic Dynamics and Control, Elsevier, vol. 21(4-5), pages 753-782, May.
    26. Boulier, Jean-Francois & Huang, ShaoJuan & Taillard, Gregory, 2001. "Optimal management under stochastic interest rates: the case of a protected defined contribution pension fund," Insurance: Mathematics and Economics, Elsevier, vol. 28(2), pages 173-189, April.
    27. Battocchio, Paolo & Menoncin, Francesco, 2004. "Optimal pension management in a stochastic framework," Insurance: Mathematics and Economics, Elsevier, vol. 34(1), pages 79-95, February.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Defined contribution pension fund; Minimum guarantee; Stochastic optimal control; Dynamic programming; Hamilton–Jacobi–Bellman equation; Viscosity solution; 91B28; 93E20; 49L25; C61; G11; G23;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors

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