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Multi-Period Risk Measures and Optimal Investment Policies

In: Optimal Financial Decision Making under Uncertainty

Author

Listed:
  • Zhiping Chen

    (School of Mathematics and Statistics, Xi’an Jiaotong University)

  • Giorgio Consigli

    (University of Bergamo)

  • Jia Liu

    (School of Mathematics and Statistics, Xi’an Jiaotong University)

  • Gang Li

    (School of Mathematics and Statistics, Xi’an Jiaotong University)

  • Tianwen Fu

    (School of Mathematics and Statistics, Xi’an Jiaotong University)

  • Qianhui Hu

    (School of Mathematics and Statistics, Xi’an Jiaotong University)

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.

Suggested Citation

  • Zhiping Chen & Giorgio Consigli & Jia Liu & Gang Li & Tianwen Fu & Qianhui Hu, 2017. "Multi-Period Risk Measures and Optimal Investment Policies," International Series in Operations Research & Management Science, in: Giorgio Consigli & Daniel Kuhn & Paolo Brandimarte (ed.), Optimal Financial Decision Making under Uncertainty, chapter 0, pages 1-34, Springer.
    • Handle: RePEc:spr:isochp:978-3-319-41613-7_1
    DOI: 10.1007/978-3-319-41613-7_1
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    Citations

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    Cited by:

    1. Fu, Tianwen & Zhuang, Xinkai & Hui, Yongchang & Liu, Jia, 2017. "Convex risk measures based on generalized lower deviation and their applications," International Review of Financial Analysis, Elsevier, vol. 52(C), pages 27-37.
    2. Yu Mei & Zhiping Chen & Jia Liu & Bingbing Ji, 2022. "Multi-stage portfolio selection problem with dynamic stochastic dominance constraints," Journal of Global Optimization, Springer, vol. 83(3), pages 585-613, July.
    3. Zhang, Ning & Su, Xiaoman & Qi, Shuyuan, 2023. "An empirical investigation of multiperiod tail risk forecasting models," International Review of Financial Analysis, Elsevier, vol. 86(C).
    4. Stefania Corsaro & Valentina De Simone & Zelda Marino & Francesca Perla, 2020. "$$l_1$$ l 1 -Regularization for multi-period portfolio selection," Annals of Operations Research, Springer, vol. 294(1), pages 75-86, November.

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