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

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.

Robust equilibrium control-measure policy for a DC pension plan with state-dependent risk aversion under mean-variance criterion

“…The intuition behind this risk aversion function is clear: the larger the current wealth level after contribution, the less risk-averse of the fund manager. Similar to the discussion in Wang and Chen [42], our choice of the risk aversion function is reasonable from both the dimensional analysis and the economic point of view. D t,x,l (Q||P) ≥ 0 is the generalized Kullback-Leibler (KL) divergence between Q and P, which is introduced to regularize the choices of Q.…”

Time-Consistent Investment-Reinsurance Strategies for the Insurer and the Reinsurer under the Generalized Mean-Variance Criteria

“…In the following, we want to check the above conclusions whether is true when the risk aversion coefficient appears in other forms. Inspired by Wang and Chen [28], we assume the risk aversion coefficients are described by the following linear functions:…”

Time-Consistent Strategies for the Generalized Multiperiod Mean-Variance Portfolio Optimization Considering Benchmark Orientation

“…Compared with the precommitment strategy, the time-consistent strategy might be adopted by the investors who are more rational and sophisticated, since the decision-makers take possible future revisions into account (e.g., Basak and Chabakauri [22], Wu and Chen [23]), Cui et al [24] and so on). For this research topic, readers may refer to Basak and Chabakauri [22], Bensoussan et al [25], Björk and Murgoci [26], Wu and Chen [23], Zhou et al [27] and Wang and Chen [28] and so on. Actually, most of the existing researches on the time-consistent strategies for the multi-period portfolio optimization problems are only concerned with the capital pool with both risky assets and one risk-free asset.…”