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.Hindawi

A new risk measure fully based on historical data is proposed, from which we can naturally derive concentrated optimal portfolios rather than imposing cardinality constraints. The new risk measure can be expressed as a quadratics of the introduced greedy matrix, which takes investors' joint behavior into account. We construct distribution‐free portfolio selection models in simple case and realistic case, respectively. The latest techniques for describing transaction cost constraints and solving nonconvex quadratic programs are utilized to obtain the optimal portfolio efficiently. In order to show the practicality, efficiency, and robustness of our new risk measure and corresponding portfolio selection models, a series of empirical studies are carried out with trading data from advanced stock markets and emerging stock markets. Different performance indicators are adopted to comprehensively compare results obtained under our new models with those obtained under the mean‐variance, mean‐semivariance, and mean‐conditional value‐at‐risk models. Out‐of‐sample results sufficiently show that our models outperform the others and provide a simple and practical approach for choosing concentrated, efficient, and robust portfolios. Copyright © 2014 John Wiley & Sons, Ltd.

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.