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Pinto, A.A., Duarte, I., Pinheiro, D. and Pliska, S.R. (2011) An Overview of Optimal Life Insurance, Consumption and Investment Problems. In: Peixoto, M., Pinto, A. and Rand, D., Eds., Dynamics, Games and Science I, Springer Proceedings in Mathematics, Springer, Berlin, 271-286. https://doi.org/10.1007/978-3-642-11456-4_18

has been cited by the following article:

• TITLE: Stochastic Analysis on Optimal Portfolio Selection for DC Pension Plan with Stochastic Interest and Inflation Rate

  AUTHORS: Kenneth Tiro, Othusitse Basimanebotlhe, Elias R. Offen

  KEYWORDS: Investment, Consumption, Hamilton-Jacobi-Bellman Equation, Defined Contribution Pension Fund, CARA Utility Function

  JOURNAL NAME: Journal of Mathematical Finance, Vol.11 No.4, November 5, 2021

  ABSTRACT: In this paper, we study optimal investment, consumption and portfolio choice in a framework where the pension planner member (PPM) embarks on an investment policy to cover up for some certain life targets. The aim of the pension plan manager is to maximize the expectation of total wealth at the time of retirement. The investment return process comprises of risk free asset and two risky assets, and the PPM benefit lies in a complete market that is constrained by the inflation rate. Explicit solutions for constant absolute risk aversion utility functions are obtained and optimal strategies are derived by applying by dynamic programming on the Hamilton-Jacobi-Bellman (HJB) equations. Our numerical results show various effects of some economic parameters on the optimal strategies. The inflation price market risk governs the amount invested in both stock and bond, at the same time varying the premium ratio (η), causes effects on the investment returns. We also investigated the effects of the correlation coefficient (ρ) when set high on consumption rate and income rate. Finally a sensitivity analysis is graphically presented.