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.
BühlmannH., Mathematical methods in risk theory, SpringerBerlin, 1970.
2.
GerberH., On additive premium calculation principles, Astin Bulletin7 (1974), 215–222.
3.
GerberH., A characterization of certain families of distributions via esscher transforms and independence, Journal of the American Statistical Association75 (1980), 1015–1018.
4.
HaezendonckJ., GoovaertsM., A new premium calculation principle based on Orlicz norms, Insurance: Mathematics and Economics1 (1982), 41–53.
5.
WangS., Premium calculation by tranforming the layer premium density, Astin Bulletin26 (1996), 71–92.
6.
YaariM., The dual theory of choice under risk, Econometrica55 (1987), 95–115.
7.
YoungV., Premium Principles, Encyclopedia of Actuarial Science, NewYork: John Wiley and Sons, 1322–1331, 2004.
8.
MorgensternO., NeumannJ.V., Theory of games and economic behaviour, Princeton University Press, 1947.
9.
TrowbridgeC., Fundamental concepts of actuarial science, Actuarial Education and Research Fund, 1989.
10.
BorchK., The mathematical theory of insurance, Lexington Mass, 1974.
11.
SchoemakerJ., The expected utility model: its variants, purposes, evidence and limitations, Journal of Economic Literature20(2) (1982), 529–563.
12.
RabinM., Risk aversion and expected-utility theory: a calibration theorem, Econometrica68(5) (2000), 1281–1292.
ZhangY., ZengJ., WenL., Approximate reliability estimation of risk premium in variance premium principle, Statistics and Decision19 (2019), 74–78.
15.
DuM., WenL., Statistical inferences of risk premium under generalized exponential premium theory, Chinese Journal of Applied Probability and Statistics35(6) (2019), 558–572.
16.
ZhangY., ZengJ., WenL., Efficiency comparison of Bayesian estimation and reliability estimation, Statistics and Decision6 (2021), 28–32.
17.
ZhangY., WenL., LiZ., The empirical Bayesian estimate of claim development factor in liability reservemodel, Acta Mathematics Applicatae Sinica45(2) (2022), 266–280.
18.
ZhangY., The posterior ratemaking of premium in binary Bayesian collective risk model, Chinese Journal of Applied Probability and Statistics38(2) (2022), 237–252.
19.
ZhangL., WenL., Approximate Bayes estimation of scale parameter of two-parameter exponential distribution, Statistics and Decision13 (2022), 52–57.
DongW., PengJ., Distribution of several kinds of insurance claims in uncertain environment, Journal of Huanggang Normal University30(3) (2010), 14–17.
22.
LiS., PengJ., ZhangB., The uncertain premium principle based on the distortion function, Insurance: Mathematics and Economics53 (2013), 317–324.
23.
LiuY., LiX., LiuY., The bounds of premium and optimality of stop loss insurance under uncertain random environments, Insurance: Mathematics and Economics64 (2015), 273–278.
24.
ShenY., YaoK., A mean-reverting currency model in an uncertain environment, Soft Computing20(10) (2016), 4131–4138.
25.
GaoJ., LiuH., Pricing longevity bonds under the uncertainty theory framework, International Journal ofPattern Recognition and Artificial Intelligence33(6) (2019), 1–30.
26.
LiuZ., YangX., Uncertain insurance risk process with single premium and multiple classes of claims, Journal of Ambient Intelligence and Humanized Computing12 (2021), 7685–7702.
27.
LiuB., Some research problems in uncertainty theory, Journal of Uncertain Systems3(1) (2009), 3–10.
28.
LiuB., Uncertainty theory: a branch of mathematics for modeling human uncertainty, Springer-VerlagBerlin, 2010.
29.
GuerraM., CentenoM., Optimal reinsurance for variance related premium calculation principles, Cambridge University Press40(1) (2010), 97–121.
30.
LiS., PengJ., The premium of uncertain risk based on expected utility, Proceedings of the China Youth Information and management scholars Conference15 (2013), 1–6.
