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Optimal Investment Strategy for Defined Contribution Pension Scheme under the Heston Volatility Model
Department of Mathematics and Statistics, Caritas University, Amorji-Nike, Nigeria
Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria
Department of Mathematics, Plateau State University, Bokkos, Nigeria
Department of Insurance, University of Jos, Jos, Nigeria
- 1 Department of Mathematics and Statistics, Caritas University, Amorji-Nike, Nigeria
- 2 Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria
- 3 Department of Mathematics, Plateau State University, Bokkos, Nigeria
- 4 Department of Insurance, University of Jos, Jos, Nigeria
Journal of Mathematical Finance·Volume 08 (2018)·Pages 613–622·Published 29 September 2018·DOI10.4236/jmf.2018.84039
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Abstract
In this paper, the optimal investment strategy for a defined contribution (DC) pension scheme was modeled with the assumption that the fund is invested partly in riskless assets and partly in risky assets. The market has a constant interest rate, a stochastic volatility that follows the Heston model, the salary is assumed constant over the entire career of the Pension Plan Participant (PPP) and the contribution is a constant proportion of the salary. The CRRA utility function was utilized to obtain a Hamilton-Jacobi-Bellman (HJB) equation. The resulting HJB equation was solved using the Prandtl Asymptotic Matching Method following the works in the literature.
KeywordsDefined Contributory Pension SchemeStochastic VolatilityCRRAPrandtl Asymptotic MatchingOptimal Investment StrategyHJB
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