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Multi-Period Risk Measures and Optimal Investment Policies

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Optimal Financial Decision Making under Uncertainty

Abstract

This chapter provides an in-depth overview of an extended set of multi-period risk measures, their mathematical and economic properties, primarily from the perspective of dynamic risk control and portfolio optimization. The analysis is structured in four parts: the first part reviews characterizing properties of multi-period risk measures, it examines their financial foundations, and clarifies cross-relationships. The second part is devoted to three classes of multi-period risk measures, namely: terminal, additive and recursive. Their financial and mathematical properties are considered, leading to the proposal of a unifying representation. Key to the discussion is the treatment of dynamic risk measures taking their relationship with evolving information flows and time evolution into account: after convexity and coherence, time consistency emerges as a key property required by risk measures to effectively control risk exposure within dynamic programs. In the third part, we consider the application of multi-period measures to optimal investment policy selection, clarifying how portfolio selection models adapt to different risk measurement paradigms. In the fourth part we summarize and point out desirable developments and future research directions. Throughout the chapter, attention is paid to the state-of-the-art and methodological and modeling implications.

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Acknowledgements

The authors are grateful to two anonymous reviewers for their detailed and stimulating comments, which have helped us to improve the chapter significantly in both content and style. This research was supported by the National Natural Science Foundation of China (Grant Numbers 70971109, 71371152 and 11571270).

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Chen, Z., Consigli, G., Liu, J., Li, G., Fu, T., Hu, Q. (2017). Multi-Period Risk Measures and Optimal Investment Policies. In: Consigli, G., Kuhn, D., Brandimarte, P. (eds) Optimal Financial Decision Making under Uncertainty. International Series in Operations Research & Management Science, vol 245. Springer, Cham. https://doi.org/10.1007/978-3-319-41613-7_1

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