On the optimal asset allocation strategy for a defined contribution pension system with refund clause of premium with predetermined interest under Heston's volatility model

2022

One of the major challenges faced by most pension fund managers in the defined pension (DC) scheme is how best member’s contributions can be invested to yield maximum returns. To achieve this, there is need to model and developed a robust investment plan which takes into consideration the volatility of the stock market price, tax on investment on risky assets and the mortality risk of its members. Based on this, the optimal portfolio distribution of a DC pension scheme with return of premium clause is studied where the mortality force function is characterized by the Weibull model and the investment in risky asset is subject to a certain proportion of tax. A portfolio with a risk-free asset and a risky asset modeled by the geometric Brownian motion such that the remaining accumulations are equally distributed between the remaining members is considered. Furthermore, the game theoretic approach is used to establish an optimization problem from the extended Hamilton Jacobi Bellman (HJB) equation which is a non-linear partial differential equation (PDE). Using variable separation method, closed form solutions of the optimal portfolio distribution and the efficient frontier are obtained. Lastly, some numerical simulations are used to study the impact of some the parameters on the optimal portfolio distribution with observations that the optimal portfolio distribution developed by the fund manager is inversely proportional to the tax imposed on the risky asset, risk averse coefficient, initial fund size, and risk free interest rate but directly proportional to time.

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modelling and Optimization of Portfolio in a DC Scheme with Return of Contributions and Tax using Weibull Force Function

Njoku

2022

“…[6], studied optimal investment plan for four different assets modelled by geometric Brownian motion whose return of contributions was with risk free interest. [7], studied investment strategies when the returned contributions are with predetermined interest; they assumed that the return contributions are with risk free interest. In this paper, we study the optimal investment plan with refund of contributions with stochastic salary and stochastic interest rate which is of affine structure.…”

Section: Introductionmentioning

confidence: 99%

DC Pension Plan with Refund of Contributions under Affine Interest Rate Model

Ini

Mandah

2020

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.

“…[8], studied equilibrium investment strategy for DC pension plan with default risk and return of premiums clauses under (CEV) model; they considered investments in treasury, stock and bond. [9], studied optimal investment plan for a pension plan when the returned contributions are with predetermined interest; they considered investment in a risk free and a risky asset and assume the risky asset is modelled by Heston volatility model. [10], investigated investment plan with return of premium clauses under inflation risk and volatility risk; they considered investment in a risk free asset, the inflation index bond and the stock whose price was modelled by Heston volatility [11], studied optimal portfolio strategies with four assets modelled by geometric Brownian motion when the return premium is with interest and the remaining accumulated wealth are equally distributed among the surviving members.…”

Section: Introductionmentioning

confidence: 99%

On Application of Matlab on Efficient Portfolio Management for a Pension Plan in the Presence of Uneven Distributions of Accumulated Wealth

Obasi

2020

In this paper, we solved the problem encountered by a pension plan member whose portfolio is made up of one risk free asset and three risky assets for the optimal investment plan with return clause and uneven distributions of the remaining accumulated wealth. Using mean variance utility function as our objective function, we formulate our problem as a continuous-time mean–variance stochastic optimal control problem. Next, we used the variational inequalities methods to transform our problem into Markovian time inconsistent stochastic control, to determine the optimal investment plan and the efficient frontier of the plan member. Using mat lab software, we obtain numerical simulations of the optimal investment plan with respect to time and compare our results with an existing result.