TY - JOUR
T1 - Bivariate distribution regression with application to insurance data
AU - Wang, Yunyun
AU - Oka, Tatsushi
AU - Zhu, Dan
N1 - Funding Information:
We would like to thank helpful comments from the editor and two anonymous referees. We are grateful to Angelos Dassios, Jiti Gao, Constantinos Kardaras, Nadja Klein, Jonas Meier, Ryo Okui, Peng Shi, Qiwei Yao, and other participants of the seminars at the London School of Economics and Political Science and the University of Melbourne, the 2021 IME conference, and the 2022 Asian Meeting of the Econometric Society in East and South-East Asia for their helpful comments and suggestions. Oka gratefully acknowledges financial support from the Australian Government through the Australian Research Council's Discovery Projects (project DP190101152).
Funding Information:
We would like to thank helpful comments from the editor and two anonymous referees. We are grateful to Angelos Dassios, Jiti Gao, Constantinos Kardaras, Nadja Klein, Jonas Meier, Ryo Okui, Peng Shi, Qiwei Yao, and other participants of the seminars at the London School of Economics and Political Science and the University of Melbourne, the 2021 IME conference, and the 2022 Asian Meeting of the Econometric Society in East and South-East Asia for their helpful comments and suggestions. Oka gratefully acknowledges financial support from the Australian Government through the Australian Research Council's Discovery Projects (project DP190101152 ).
Publisher Copyright:
© 2023 The Author(s)
PY - 2023/11
Y1 - 2023/11
N2 - Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given observed circumstances. This article presents an estimation method for modeling the conditional joint distribution of bivariate outcomes based on the distribution regression and factorization methods. This method is considered semiparametric in that it allows for flexible modeling of both the marginal and joint distributions conditional on covariates without imposing global parametric assumptions across the entire distribution. In contrast to existing parametric approaches, our method can accommodate discrete, continuous, or mixed variables, and provides a simple yet effective way to capture distributional dependence structures between bivariate outcomes and covariates. Various simulation results confirm that our method can perform similarly or better in finite samples compared to the alternative methods. In an application to the study of a motor third-party liability insurance portfolio, the proposed method effectively estimates risk measures such as the conditional Value-at-Risk and Expected Shortfall. This result suggests that this semiparametric approach can serve as an alternative in insurance risk management.
AB - Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given observed circumstances. This article presents an estimation method for modeling the conditional joint distribution of bivariate outcomes based on the distribution regression and factorization methods. This method is considered semiparametric in that it allows for flexible modeling of both the marginal and joint distributions conditional on covariates without imposing global parametric assumptions across the entire distribution. In contrast to existing parametric approaches, our method can accommodate discrete, continuous, or mixed variables, and provides a simple yet effective way to capture distributional dependence structures between bivariate outcomes and covariates. Various simulation results confirm that our method can perform similarly or better in finite samples compared to the alternative methods. In an application to the study of a motor third-party liability insurance portfolio, the proposed method effectively estimates risk measures such as the conditional Value-at-Risk and Expected Shortfall. This result suggests that this semiparametric approach can serve as an alternative in insurance risk management.
KW - Distribution regression
KW - Finance
KW - Multivariate statistics
KW - Risk management
KW - Semiparametric approach
UR - http://www.scopus.com/inward/record.url?scp=85171264164&partnerID=8YFLogxK
U2 - 10.1016/j.insmatheco.2023.08.005
DO - 10.1016/j.insmatheco.2023.08.005
M3 - Article
AN - SCOPUS:85171264164
SN - 0167-6687
VL - 113
SP - 215
EP - 232
JO - Insurance: Mathematics and Economics
JF - Insurance: Mathematics and Economics
ER -