On the Maximization of Investment Portfolios with Returns of Contributions

Authors

  • Edikan E. Akpanibah Department of Mathematics and Statistics, Federal University Otuoke, Bayelsa, Nigeria.
  • Bright O. Osu Department of Mathematics, Michael Ok para University of Agriculture Umudike
  • Ben I. Oruh Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria
  • Okonkwo C. Ukwuoma Department of Mathematics and Statistics, Caritas University Amorji Nike. Enugu
  • and Everestus O. Eze Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria.

Keywords:

interest rate, game theoretic approach, return of contributions, optimal control plan, extended HJB equation, Pension scheme

Abstract

In this work, how investment portfolios of a pension scheme can be maximized in the presence of the return clause of contributions is presented. This clause permits the return of accumulated contributions together with predetermined interest from risk-free assets to members’ families whenever death occurs to their family members. Also considered
herein are investments in cash, marketable security, and loan to increase the total accumulated funds of the pension scheme left to be distributed among the surviving members such that the price models of marketable security and loan follow geometric Brownian motions. The game-theoretic approach, separation of variable technique, and mean-variance utility are used to obtain closed-form solutions of the optimal control plans for the assets and the efficient frontier. Next, the consequence of some parameters on the optimal control plans with time is numerically analysed. Furthermore, a theoretical comparison of our result with an existing result is given.

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Author Biographies

Edikan E. Akpanibah, Department of Mathematics and Statistics, Federal University Otuoke, Bayelsa, Nigeria.

Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria.

Okonkwo C. Ukwuoma, Department of Mathematics and Statistics, Caritas University Amorji Nike. Enugu

Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria.

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Published

2020-08-31

How to Cite

Edikan E. Akpanibah, Bright O. Osu, Ben I. Oruh, Okonkwo C. Ukwuoma, & and Everestus O. Eze. (2020). On the Maximization of Investment Portfolios with Returns of Contributions. MathLAB Journal, 6, 1-16. Retrieved from https://purkh.com/index.php/mathlab/article/view/806

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Section

Research Articles

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