Multiplicative parameters and estimators: applications in economics and finance.

*(English)*Zbl 1347.62225Summary: In this paper, we pay our attention to multiplicative parameters of random variables and their estimators. We study multiplicative properties of the multiplicative expectation and multiplicative variation as well as their estimators. For distributions having applications in finance and insurance we provide their multiplicative parameters and their properties. We consider, among others, heavy-tailed distributions such as lognormal and Pareto distributions, applied to the modelling of large losses. We discuss multiplicative models, in which the geometric mean and the geometric standard deviation are more natural than their arithmetic counterparts. We provide two examples from the Warsaw Stock Exchange in 1995–2009 and from a bid of 52-week treasury bills in 1992–2009 in Poland as an illustrative example.

##### MSC:

62P05 | Applications of statistics to actuarial sciences and financial mathematics |

62P20 | Applications of statistics to economics |

##### Keywords:

geometric mean; geometric variance; lognormal distribution; Pareto distribution; multiplicative estimators
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\textit{H. Jasiulewicz} and \textit{W. Kordecki}, Ann. Oper. Res. 238, No. 1--2, 299--313 (2016; Zbl 1347.62225)

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##### References:

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