The premium of uncertain risk based on standard deviation principle

Article type: Research Article

Authors: Zhang, Yunqi | Sheng, Yuhong^{; *}

Affiliations: College of Mathematics and System Science, Xinjiang University, Urumqi, China

Correspondence: [*] Corresponding author. Yuhong Sheng, College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China. Tel.: +86 18167978160; E-mail: [email protected].

Abstract:  Risk measurement and insurance pricing have always been issues of concern in actuarial science. Under the framework of uncertainty theory, this paper puts forward a new premium principle: uncertain standard deviation premium principle, proposes some of its properties about risk and compares the premiums of different risks. Based on the utility function of risk aversion, the additional premium coefficient is derived and two specific numerical examples are used to calculate the maximum premium. Furthermore, the unknown parameters of the policy with deductible are estimated by uncertain moment estimation and uncertain maximum likelihood estimation.

Keywords: Uncertainty theory, standard deviation premium principle, additional premium coefficient, utility function, parameter estimation

DOI: 10.3233/JIFS-223297

Journal: Journal of Intelligent & Fuzzy Systems, vol. 44, no. 6, pp. 9965-9975, 2023