Abstract
Through the composition of two real-valued functions, we propose a new class of multi-period risk measure which is time consistent. The new multi-period risk measure is monotonous and convex when the two real-valued functions satisfy monotonicity and convexity. Based on this generic framework, we construct a specific class of time-consistent multi-period risk measure by considering the lower partial moment between the realized wealth and the target wealth at individual periods. With the new multi-period risk measure as the objective function, we formulate a multi-period portfolio selection model by considering transaction costs at individual investment periods. Furthermore, this stochastic programming model is transformed into a deterministic programming problem using the scenario tree technology. Finally, we show through empirical tests and comparisons the rationality, practicality and efficiency of our new multi-period risk measure and the corresponding portfolio selection model.
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Acknowledgments
The authors are grateful to two anonymous reviewers and the editor-in-chief for their constructive comments, which have helped us to improve the paper significantly. This research was supported by the National Natural Science Foundation of China (Grant Numbers 70971109, 71371152 and 11571270).
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Chen, Z., Liu, J., Li, G. et al. Composite time-consistent multi-period risk measure and its application in optimal portfolio selection. TOP 24, 515–540 (2016). https://doi.org/10.1007/s11750-015-0407-7
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DOI: https://doi.org/10.1007/s11750-015-0407-7