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Optimal Investment And Optimal Additional Voluntary Contribution Rate Of A Dc Pension Fund In A Jump-Diffusion Environment

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  • CHARLES I. NKEKI

    (Department of Mathematics, Faculty of Physical Sciences, University of Benin, P.M.B. 1154, Benin City, Edo State, Nigeria)

Abstract

This paper considers an optimal investment and an optimal additional contribution rate of a pension plan member (PPM) who faces both diffusion and jump risks in a defined contribution (DC) pension plan. We put into consideration three background risks which include interest rate, investment and salary risks. The stock prices, interest rate and salary process of a PPM are allowed to follow a jump-diffusion process. A PPM is expected to make two kind of contributions: compulsory and additional voluntary contributions. The compulsory one is a fixed proportion of a PPM's salary and the additional one is voluntary which is time and interest rate dependent. The aims of the investor is to determine the optimal investment and optimal contribution rate in a jump-diffusion environment. In order to obtain the optimal investment and optimal contribution rate, the resulting wealth process was transformed into Hamilton–Jacobi–Bellman equation by the method of dynamic programming. As a result, the optimal investment and optimal contribution rate of a PPM were obtained. Furthermore, some empirical analyses were conducted and results obtained. We found that the optimal investment ultimately depend on stocks diffusion and jump risks, interest rate and salary risks, optimal contribution rate and the salary process. The contribution rate of a PPM was found to depend on the investment strategies, salary process and interest rate risks, salary and its growth rate and CRRA coefficient. We also found that the contribution rate depends inversely on the salary process of a PPM over time.

Suggested Citation

  • Charles I. Nkeki, 2017. "Optimal Investment And Optimal Additional Voluntary Contribution Rate Of A Dc Pension Fund In A Jump-Diffusion Environment," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 12(04), pages 1-26, December.
    • Handle: RePEc:wsi:afexxx:v:12:y:2017:i:04:n:s2010495217500178
    DOI: 10.1142/S2010495217500178
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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. 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.
    3. Hainaut, Donatien & Deelstra, Griselda, 2014. "Optimal timing for annuitization, based on jump diffusion fund and stochastic mortality," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 124-146.
    4. Gao, Jianwei, 2008. "Stochastic optimal control of DC pension funds," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1159-1164, June.
    5. Paolo BATTOCCHIO, 2002. "Optimal Portfolio Strategies with Stochastic Wage Income : The Case of A defined Contribution Pension Plan," LIDAM Discussion Papers IRES 2002005, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    6. Bjarne Astrup Jensen & Carsten Sørensen, 2001. "Paying for Minimum Interest Rate Guarantees: Who Should Compensate Who?," European Financial Management, European Financial Management Association, vol. 7(2), pages 183-211, June.
    7. An Chen & Filip Uzelac, 2015. "Portability, Salary and Asset Price Risk: A Continuous-Time Expected Utility Comparison of DB and DC Pension Plans," Risks, MDPI, vol. 3(1), pages 1-26, March.
    8. 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.
    9. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    10. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    11. Cairns, Andrew, 2000. "Some Notes on the Dynamics and Optimal Control of Stochastic Pension Fund Models in Continuous Time," ASTIN Bulletin, Cambridge University Press, vol. 30(1), pages 19-55, May.
    12. Griselda Deelstra & Martino Grasselli & Pierre-François Koehl, 2000. "Optimal investment strategies in a CIR framework," ULB Institutional Repository 2013/7594, ULB -- Universite Libre de Bruxelles.
    13. Battocchio, Paolo & Menoncin, Francesco, 2004. "Optimal pension management in a stochastic framework," Insurance: Mathematics and Economics, Elsevier, vol. 34(1), pages 79-95, February.
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    Cited by:

    1. Henrique Ferreira Morici & Elena Vigna, 2023. "Optimal additional voluntary contribution in DC pension schemes to manage inadequacy risk," Carlo Alberto Notebooks 699 JEL Classification: C, Collegio Carlo Alberto.

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