Abstract
Risk aversion, which refers to the reluctant attitude of an economic agent to accept uncertain outcomes compared with a certain one even if the latter has a lower outcome in monetary value, plays a fundamental role in decision theory and risk management. This paper investigates how to measure different agents’ risk-averse attitudes towards a risky situation consisting of multiple uncertain components under uncertainty theory. First, a general method to approximately compute the multivariate uncertain risk premium is proposed. Subsequently, the multivariate uncertain risk aversion is formally defined based on the multivariate uncertain risk premium, and the corresponding sufficient condition for utility functions being multivariate risk-averse is given. Its relation to Richard’s correlation aversion under the framework of uncertainty theory is also discussed. Finally, the suggested theoretical findings are applied to an accounts receivables (ARs) pricing problem to exhibit their applicability. The results show that our method is more applicable in practice than the univariate approach. Moreover, for the AR financing, the AR owner should choose higher-credit trading partners and financial institutions with less risk aversion to cooperate for acquiring more cash.
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Funding
This work was supported by grants from the National Natural Science Foundation of China (No. 71872110 and No. 71771177) and Innovation Fund for University Production, Education and Research from China’s Ministry of Education (No. 2019J01012).
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K. Wang and M. Zhao conceptualized the study; X. Huang and M. Zhao formally analysed the study; M. Zhao helped in methodology; X. Huang and S. Hu wrote the original draft; K. Wang and M. Zhao were involved in writing—review and editing; H. Wang and J. Zhou acquired the funding; S. Hu developed the software; K. Wang supervised the study; H. Wang and J. Zhou validated the study.
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Wang, K., Huang, X., Hu, S. et al. Multivariate uncertain risk aversion with application to accounts receivables pricing. Soft Comput 26, 9465–9480 (2022). https://doi.org/10.1007/s00500-022-07272-9
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DOI: https://doi.org/10.1007/s00500-022-07272-9