TITLE:
Laws of Large Numbers for Dynamic Coherent Risk Measures
AUTHORS:
Zengjing Chen, Yiwei Lin, Zhijie Xiao, Guodong Zhang
KEYWORDS:
Dynamic Coherent Risk Measures, Time Consistency, Law of Large Numbers
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.12 No.1,
February
28,
2022
ABSTRACT: In this paper, we study the asymptotic behavior of dynamic coherent risk measures in general settings regardless of specific representations of the risk measures. In particular, we develop three different types laws of large numbers (LLN) for the average values of portfolios. These LLNs capture the limiting behavior of time-consistent dynamic coherent risk measures under appropriate conditions. Our results apply to general probability spaces with a sequence of financial returns characterized by a set of probability measures. We show that the limit of these averages will generally be multivalued within an identified set. We give examples to illustrate the potential applicability of our results and derive asymptotic results on estimation for the risk of returns of financial assets using a time-consistent dynamic coherent risk measure induced by a class of g-expectations.