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Mathematics 2019, 7(1), 108; https://doi.org/10.3390/math7010108

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

1,2
and
1,2,*
1
School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, Shaanxi, China
2
Center for Optimization Technique and Quantitative Finance, Xi’an International Academy for Mathematics and Mathematical Technology, Xi’an 710049, Shaanxi, China
*
Author to whom correspondence should be addressed.
Received: 30 November 2018 / Revised: 6 January 2019 / Accepted: 18 January 2019 / Published: 21 January 2019
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Abstract

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. View Full-Text
Keywords: DC pension plan; state-dependent risk aversion; mean-variance optimization; stochastic control; extended Bellman equation DC pension plan; state-dependent risk aversion; mean-variance optimization; stochastic control; extended Bellman equation
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Wang, L.; Chen, Z. Stochastic Game Theoretic Formulation for a Multi-Period DC Pension Plan with State-Dependent Risk Aversion. Mathematics 2019, 7, 108.

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