scholarly journals Nash Equilibrium Strategy for a DC Pension Plan with State-Dependent Risk Aversion: A Multiperiod Mean-Variance Framework

2018 ◽  
Vol 2018 ◽  
pp. 1-17 ◽  
Author(s):  
Liyuan Wang ◽  
Zhiping Chen
Keyword(s):  
Risk Aversion ◽  
Pension Plan ◽  
Time Inconsistency ◽  
Equilibrium Strategy ◽  
Defined Contribution ◽  
Nash Equilibrium Strategy ◽  
State Dependent ◽  
Special Cases ◽  
Fractional Function ◽  
Mean Variance

This paper investigates a defined contribution (DC) pension plan investment problem during the accumulation phase under the multiperiod mean-variance criterion. Different from most studies in the literature, where the investor’s risk aversion attitude is state-independent, we choose a state-dependent risk aversion parameter, which is a fractional function of the current wealth level. Moreover, we incorporate the wage income factor into our model, which leads to a more complicated problem than the portfolio selection problems that appeared in relevant papers. Due to the time inconsistency of the resulting problem, we derive the explicit expressions for the equilibrium strategy and the corresponding equilibrium value function by adopting the game theoretic framework and using the extended Bellman equation. Further, two special cases are discussed. Finally, based on real data from the American market, some prominent features of the equilibrium strategy established in our theoretical derivations are provided by comparing them with the results in the existing literature.

scholarly journals Stochastic Game Theoretic Formulation for a Multi-Period DC Pension Plan with State-Dependent Risk Aversion

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 108 ◽  
Author(s):  
Liyuan Wang ◽  
Zhiping Chen
Keyword(s):  
Risk Aversion ◽  
Stochastic Game ◽  
Pension Plan ◽  
Time Inconsistency ◽  
State Variables ◽  
Economic Point ◽  
State Dependent ◽  
Equilibrium Control ◽  
Special Cases ◽  
Game Theoretic

When facing a multi-period defined contribution (DC) pension plan investment problem during the accumulation phase, the risk aversion attitude of a mean-variance investor may depend on state variables. In this paper, we propose a state-dependent risk aversion model which is a linear function of the current wealth level after contribution. This risk aversion model is reasonable from both the dimensional analysis and the economic point of view. Moreover, we incorporate the wage income factor into our model. In the field of dynamic investment analysis, most studies have irrational situations in their models because of the lack of the positiveness for the wealth process. In view of it, we further improve the work of Wang and Chen by completely eliminating the irrationality of the model. Due to the time-inconsistency of the resulting stochastic control problem, we derive the explicit expressions of the equilibrium control and the corresponding equilibrium value function by adopting the game theoretic framework developed in Björk and Murgoci. Further, two special cases are discussed. Finally, using a more realistic risk aversion coefficient, we provide a series of empirical tests based on the real data from the American market and compare our results with the relevant results in the literature.

scholarly journals Optimal Portfolio Selection of Mean-Variance Utility with Stochastic Interest Rate

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Shuang Li ◽  
Shican Liu ◽  
Yanli Zhou ◽  
Yonghong Wu ◽  
Xiangyu Ge
Keyword(s):  
Optimal Control ◽  
Interest Rate ◽  
Differential Equations ◽  
Risk Aversion ◽  
Hjb Equation ◽  
Time Inconsistency ◽  
Equilibrium Strategy ◽  
Stochastic Interest Rate ◽  
Stochastic Interest ◽  
Mean Variance

In order to tackle the problem of how investors in financial markets allocate wealth to stochastic interest rate governed by a nested stochastic differential equations (SDEs), this paper employs the Nash equilibrium theory of the subgame perfect equilibrium strategy and propose an extended Hamilton-Jacobi-Bellman (HJB) equation to analyses the optimal control over the financial system involving stochastic interest rate and state-dependent risk aversion (SDRA) mean-variance utility. By solving the corresponding nonlinear partial differential equations (PDEs) deduced from the extended HJB equation, the analytical solutions of the optimal investment strategies under time inconsistency are derived. Finally, the numerical examples provided are used to analyze how stochastic (short-term) interest rates and risk aversion affect the optimal control strategies to illustrate the validity of our results.

The effects of risk aversion and density of contribution on comparisons of administrative charges in individual account pension systems

2016 ◽  
Vol 16 (1) ◽  
pp. 1-20 ◽  
Author(s):  
LUIS CHAVEZ-BEDOYA
Keyword(s):  
Risk Aversion ◽  
Pension System ◽  
Pension Plan ◽  
Defined Contribution ◽  
Individual Retirement Accounts ◽  
Terminal Wealth ◽  
Individual Account ◽  
Retirement Accounts ◽  
Defined Contribution Pension Plan ◽  
Accumulation Phase

AbstractThis paper studies the effects of risk aversion and density of contribution (DoC) on comparisons of proportional charges on flow (contributions) and balance (assets) during the accumulation phase of a defined-contribution pension plan in a system of individual retirement accounts. If the participant's degree of risk aversion increases and both charges yield the same expected terminal wealth, then the charge on balance improves with respect to the charge on flow when performing comparisons that examine the ratio between the resulting expected utilities of terminal wealth. When this methodology is applied to the Peruvian Private Pension System, empirical results demonstrate that the aforementioned result also holds for arbitrary charges on flow and balance and that the effect of DoC on these comparisons is nearly negligible for most of the assessed scenarios.

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.

Mean-Variance Asset Liability Management with State-Dependent Risk Aversion

2017 ◽  
Vol 21 (1) ◽  
pp. 87-106 ◽  
Author(s):  
Yan Zhang ◽  
Yonghong Wu ◽  
Shuang Li ◽  
Benchawan Wiwatanapataphee
Keyword(s):  
Risk Aversion ◽  
Asset Liability Management ◽  
Liability Management ◽  
State Dependent ◽  
Mean Variance
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