scholarly journals Equilibrium Investment Strategy for DC Pension Plan with Inflation and Stochastic Income under Heston’s SV Model

2016 ◽  
Vol 2016 ◽  
pp. 1-18 ◽  
Author(s):  
Jingyun Sun ◽  
Zhongfei Li ◽  
Yongwu Li
Keyword(s):  
Pension Plan ◽  
Investment Strategy ◽  
Investment Strategies ◽  
Value Functions ◽  
Defined Contribution ◽  
Hjb Equations ◽  
Plan Member ◽  
The Mean ◽  
Hamilton Jacobi Bellman ◽  
Mean Variance

We consider a portfolio selection problem for a defined contribution (DC) pension plan under the mean-variance criteria. We take into account the inflation risk and assume that the salary income process of the pension plan member is stochastic. Furthermore, the financial market consists of a risk-free asset, an inflation-linked bond, and a risky asset with Heston’s stochastic volatility (SV). Under the framework of game theory, we derive two extended Hamilton-Jacobi-Bellman (HJB) equations systems and give the corresponding verification theorems in both the periods of accumulation and distribution of the DC pension plan. The explicit expressions of the equilibrium investment strategies, corresponding equilibrium value functions, and the efficient frontiers are also obtained. Finally, some numerical simulations and sensitivity analysis are presented to verify our theoretical results.

scholarly journals Alpha-robust mean-variance investment strategy for DC pension plan with uncertainty about jump-diffusion risk

2020 ◽  
Author(s):  
Danping Li ◽  
Junna BI ◽  
Mengcong Hu
Keyword(s):  
Ambiguity Aversion ◽  
Pension Plan ◽  
Optimal Investment ◽  
Jump Diffusion ◽  
Investment Strategy ◽  
Investment Strategies ◽  
Value Functions ◽  
Defined Contribution ◽  
Optimal Investment Problem ◽  
Mean Variance

This paper considers an alpha-robust optimal investment problem for a defined contribution (DC) pension plan with uncertainty about jump and diffusion risks in a mean-variance framework. Our model allows the pension manager to have different levels of ambiguity aversion, rather than only consider the extremely ambiguity-averse attitude. Moreover, in the DC pension plan, contributions are supposed to be a predetermined amount of money as premiums and the pension funds are allowed to be invested in a financial market which consists of a risk-free asset, and a risky asset satisfying a jump-diffusion process. Notice that a part of pension members could die during the accumulation phase, and their premiums should be withdrawn. Thus, we consider the return of premiums clauses by an actuarial method and assume that the surviving members will share the difference between the return and the accumulation equally. Taking account of the pension fund size and the volatility of the accumulation, a mean-variance criterion as the investment objective for the DC plan can be formulated. By applying a game theoretic framework, the equilibrium investment strategies and the corresponding equilibrium value functions can be obtained explicitly. Economic interpretations are given in the numerical simulation, which is presented to illustrate our results.

DETERMINISTIC INVESTMENT STRATEGY IN A DC PENSION PLAN WITH INFLATION RISK UNDER MEAN-VARIANCE CRITERION

2020 ◽  
pp. 1-16
Author(s):  
Xingchun Peng ◽  
Fenge Chen
Keyword(s):  
Diffusion Process ◽  
Pension Plan ◽  
Investment Strategy ◽  
Inflation Risk ◽  
Special Cases ◽  
Plan Member ◽  
The Mean ◽  
Adapted Process ◽  
Mean Variance ◽  
Variance Criterion

This paper studies an optimal deterministic investment problem for a DC pension plan member with inflation risk. We describe the price processes of the inflation-indexed bond and the stock by a continuous diffusion process and a jump diffusion process with random parameters, respectively. The contribution rate linked to the income of the DC plan member is assumed to be a non-Markovian adapted process. Under the mean-variance criterion, we use Malliavin calculus to derive a characterization for the optimal deterministic investment strategy. In some special cases, we obtain the explicit expressions for the optimal deterministic strategies.

OPTIMAL INVESTMENT FOR A DEFINED-CONTRIBUTION PENSION SCHEME UNDER A REGIME SWITCHING MODEL

2015 ◽  
Vol 45 (2) ◽  
pp. 397-419 ◽  
Author(s):  
An Chen ◽  
Łukasz Delong
Keyword(s):  
Asset Allocation ◽  
Regime Switching ◽  
Pension Plan ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Switching Behavior ◽  
Pension Scheme ◽  
Defined Contribution ◽  
State Of The Economy ◽  
Plan Member

AbstractWe study an asset allocation problem for a defined-contribution (DC) pension scheme in its accumulation phase. We assume that the amount contributed to the pension fund by a pension plan member is coupled with the salary income which fluctuates randomly over time and contains both a hedgeable and non-hedgeable risk component. We consider an economy in which macroeconomic risks are existent. We assume that the economy can be in one ofIstates (regimes) and switches randomly between those states. The state of the economy affects the dynamics of the tradeable risky asset and the contribution process (the salary income of a pension plan member). To model the switching behavior of the economy we use a counting process with stochastic intensities. We find the investment strategy which maximizes the expected exponential utility of the discounted excess wealth over a target payment, e.g. a target lifetime annuity.

scholarly journals The Role of Inflation-indexed Bond in Optimal Management of Defined Contribution Pension Plan During the Decumulation Phrase

2018 ◽  
Author(s):  
Xiaoyi Zhang ◽  
Junyi Guo
Keyword(s):  
Pension Plan ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Programming Approach ◽  
Defined Contribution ◽  
Inflation Risk ◽  
Dynamic Programming Approach ◽  
Optimal Investment Strategy ◽  
Defined Contribution Pension Plan ◽  
Hamilton Jacobi Bellman

In this paper we investigate the optimal investment strategy for a defined contribution (DC) pension plan during the decumulation phrase which is risk-averse and pays close attention to inflation risk. The plan aims to maximize the expected constant relative risk aversion (CRRA) utility from the terminal wealth by investing the wealth in a financial market consisting of an inflation-indexed bond, an ordinary zero coupon bond and a risk-free asset. We derive the optimal investment strategy in closed-form using the dynamic programming approach by solving the corresponding Hamilton-Jacobi-Bellman (HJB) equation. Our theoretical and numerical results reveal that under some rational assumptions, an inflation-indexed bond do has significant advantage to hedge inflation risk.

scholarly journals Precommitted Investment Strategy versus Time-Consistent Investment Strategy for a General Risk Model with Diffusion

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Lidong Zhang ◽  
Ximin Rong ◽  
Ziping Du
Keyword(s):  
Risk Model ◽  
Theoretical Perspective ◽  
Optimal Strategies ◽  
Investment Strategy ◽  
Value Functions ◽  
Lagrange Method ◽  
Bellman Equations ◽  
Strategy Versus ◽  
Hamilton Jacobi Bellman ◽  
Mean Variance

We mainly study a general risk model and investigate the precommitted strategy and the time-consistent strategy under mean-variance criterion, respectively. A lagrange method is proposed to derive the precommitted investment strategy. Meanwhile from the game theoretical perspective, we find the time-consistent investment strategy by solving the extended Hamilton-Jacobi-Bellman equations. By comparing the precommitted strategy with the time-consistent strategy, we find that the company under the time-consistent strategy has to give up the better current utility in order to keep a consistent satisfaction over the whole time horizon. Furthermore, we theoretically and numerically provide the effect of the parameters on these two optimal strategies and the corresponding value functions.

scholarly journals On the Effect of Inflation and Impact of Hedging on Pension Wealth Generation Strategies under the Geometric Brownian Motion Model

2019 ◽  
pp. 119-142
Author(s):  
Bright O. Osu ◽  
Kevin N. C. Njoku ◽  
Ben I. Oruh
Keyword(s):  
Utility Function ◽  
Pension Reform ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Pension Scheme ◽  
Investment Strategies ◽  
Defined Contribution ◽  
Plan Member ◽  
The Impact ◽  
Pension Wealth

This work investigates the effect of Inflation and the impact of hedging on the optimal investment strategies for a prospective investor in a DC pension scheme, using inflation-indexed bond and inflation-linked stock. The model used here permits the plan member to make a defined contribution, as provided in the Nigerian Pension Reform Act of 2004. The pension plan member is allowed to invest in risk-free asset (cash), and two risky assets (i.e., the inflation-indexed bond and inflation-linked stock). A stochastic differential equation of the pension wealth that takes into account certain agreed proportions of the plan member’s salary, paid as contribution towards the pension fund, is constructed and presented. The Hamilton-Jacobi-Bellman (H-J-B) equation, Legendre transformation, and dual theory are used to obtain the explicit solution of the optimal investment strategies for CRRA utility function. Our investigation reveals that the inflation have significant negative effect on wealth investment strategies, particularly, the RRA(w) is not constant with the investment strategy, since the inflation parameters and coefficient of CRRA utility function have insignificant input on the investment strategies, and also the inflation-indexed bond and inflation-linked stock has a positive damping effect (hedging) on the severe effect of inflation.

scholarly journals A Multiple-Goal Investment Strategy for Sovereign Wealth Funds: An Application to China

2015 ◽  
Vol 14 (1) ◽  
pp. 78-97
Author(s):  
Li Xie ◽  
Wing Thye Woo ◽  
Zhichao Zhang ◽  
Zhuang Zhang
Keyword(s):  
Asset Allocation ◽  
Investment Strategy ◽  
Mental Accounting ◽  
Sovereign Wealth Funds ◽  
Multiple Goal ◽  
The Mean ◽  
Mean Variance ◽  
Macroeconomic Environment

This paper develops a multiple-goal investment strategy for sovereign wealth funds. In our investment strategy, we embed the Black-Litterman (B-L) model into the mean variance mental accounting (MVMA) approach. The B-L method provides a means of modeling return expectations, and the MVMA framework allows the derivation of the optimal asset allocation from a global investment perspective, in a response to a specific macroeconomic environment.

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