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

In this paper, we propose a generalized multiperiod mean-variance portfolio optimization based on consideration of benchmark orientation and intertemporal restrictions, in which the investors not only focus on their own performance but also tend to compare the performance gap between themselves and the benchmark. We aim to find the time-consistent strategy under the generalized mean-variance criterion, such that their relative performance is maximized. We derive the time-consistent strategy for the proposed model with and without a risk-free asset by using the backward induction approach. The results show that, in the case that there exists a risk-free asset, the time-consistent strategy is a feedback strategy about the benchmark process. However, in the other case, the time-consistent strategy is a double feedback strategy on both the benchmark process and the wealth process. Finally, we carry out some numerical simulations to show the evolution process of the time-consistent strategy. These simulations indicate that the proposed strategy can not only reduce the risk of investment existed in the intermediate time period but also imitate the return of the benchmark process.