TY - JOUR
T1 - Sharing the Value-at-Risk under Distributional Ambiguity
AU - Chen, Zhi
AU - Xie, Weijun
PY - 2021/1
Y1 - 2021/1
N2 - This paper considers the problem of risk sharing, where a coalition of homogeneous agents, each bearing a random cost, aggregates their costs, and shares the value-at-risk of such a risky position. Due to limited distributional information in practice, the joint distribution of agents' random costs is difficult to acquire. The coalition, being aware of the distributional ambiguity, thus evaluates the worst-case value-at-risk within a commonly agreed ambiguity set of the possible joint distributions. Through the lens of cooperative game theory, we show that this coalitional worst-case value-at-risk is subadditive for the popular ambiguity sets in the distributionally robust optimization literature that are based on (i) convex moments or (ii) Wasserstein distance to some reference distributions. In addition, we propose easy-to-compute core allocation schemes to share the worst-case value-at-risk. Our results can be readily extended to sharing the worst-case conditional value-at-risk under distributional ambiguity.
AB - This paper considers the problem of risk sharing, where a coalition of homogeneous agents, each bearing a random cost, aggregates their costs, and shares the value-at-risk of such a risky position. Due to limited distributional information in practice, the joint distribution of agents' random costs is difficult to acquire. The coalition, being aware of the distributional ambiguity, thus evaluates the worst-case value-at-risk within a commonly agreed ambiguity set of the possible joint distributions. Through the lens of cooperative game theory, we show that this coalitional worst-case value-at-risk is subadditive for the popular ambiguity sets in the distributionally robust optimization literature that are based on (i) convex moments or (ii) Wasserstein distance to some reference distributions. In addition, we propose easy-to-compute core allocation schemes to share the worst-case value-at-risk. Our results can be readily extended to sharing the worst-case conditional value-at-risk under distributional ambiguity.
KW - conditional value-at-risk
KW - distributionally robust optimization
KW - risk sharing
KW - value-at-risk
UR - http://www.scopus.com/inward/record.url?scp=85099519899&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85099519899&origin=recordpage
UR - http://www.optimization-online.org/DB_HTML/2019/06/7242.html
U2 - 10.1111/mafi.12296
DO - 10.1111/mafi.12296
M3 - 21_Publication in refereed journal
VL - 31
SP - 531
EP - 559
JO - Mathematical Finance
JF - Mathematical Finance
SN - 0960-1627
IS - 1
ER -