Open AccessDC Pension Plan with Refund of Contributions under Affine Interest Rate Model
Author(s) -
Udeme O. Ini,
Obinichi C. Mandah,
Edikan E. Akpanibah
Publication year - 2020
Publication title -
asian journal of probability and statistics
Language(s) - English
Resource type - Journals
ISSN - 2582-0230
DOI - 10.9734/ajpas/2020/v7i230175
Subject(s) - hamilton–jacobi–bellman equation , affine transformation , interest rate , geometric brownian motion , economics , bond , short rate model , pension , econometrics , stochastic volatility , mathematics , mathematical optimization , actuarial science , mathematical economics , volatility (finance) , finance , bellman equation , economy , diffusion process , pure mathematics , service (business)
This paper studies the optimal investment plan for a pension scheme with refund of contributions, stochastic salary and affine interest rate model. A modified model which allows for refund of contributions to death members’ families is considered. In this model, the fund managers invest in a risk free (treasury) and two risky assets (stock and zero coupon bond) such that the price of the risky assets are modelled by geometric Brownian motions and the risk free interest rate is of affine structure. Using the game theoretic approach, an extended Hamilton Jacobi Bellman (HJB) equation which is a system of non linear PDE is established. Furthermore, the extended HJB equation is then solved by change of variable and variable separation technique to obtain explicit solutions of the optimal investment plan for the three assets using mean variance utility function. Finally, theoretical analyses of the impact of some sensitive parameters on the optimal investment plan are presented.