TY - CHAP
T1 - Multi-period risk measures and optimal investment policies
AU - Chen, Zhiping
AU - Consigli, Giorgio
AU - Liu, Jia
AU - Li, Gang
AU - Fu, Tianwen
AU - Hu, Qianhui
N1 - Funding Information:
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).
Publisher Copyright:
© Springer International Publishing Switzerland 2017.
PY - 2017
Y1 - 2017
N2 - 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 multiperiod 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.
AB - 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 multiperiod 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.
KW - Bellman’s principle
KW - Dynamic risk control
KW - Information processes
KW - Multi-period risk measures
KW - Portfolio optimization
KW - Recoursive risk measures
KW - Time-consistency
UR - http://www.scopus.com/inward/record.url?scp=84992163228&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-41613-7_1
DO - 10.1007/978-3-319-41613-7_1
M3 - Chapter
AN - SCOPUS:84992163228
T3 - International Series in Operations Research and Management Science
SP - 1
EP - 34
BT - International Series in Operations Research and Management Science
ER -