## Tbilisi Mathematical Journal

- Tbilisi Math. J.
- Volume 6 (2013), 57-71.

### Characterization theorems for mean value insurance premium calculation principle

Mykola Pratsiovytyi and Vitaliy Drozdenko

#### Abstract

Characterization theorems for several properties possessed by the mean value insurance premium calculation principle are presented. Demonstrated theorems cover cases of additivity, consistency, iterativity, and scale invariance properties. Results are formulated in a form of necessary and sufficient conditions for attainment of the properties imposed on the auxiliary function with the help of which the mean value premium calculation principle is defined. We show also that for the mean value principle subjected to pricing of only strictly positive risks the class of the auxiliary functions producing scale invariant premiums is larger than in the general case.

#### Article information

**Source**

Tbilisi Math. J., Volume 6 (2013), 57-71.

**Dates**

Received: 9 August 2013

Revised: 11 December 2013

Accepted: 18 December 2013

First available in Project Euclid: 12 June 2018

**Permanent link to this document**

https://projecteuclid.org/euclid.tbilisi/1528768937

**Digital Object Identifier**

doi:10.32513/tbilisi/1528768937

**Mathematical Reviews number (MathSciNet)**

MR3260492

**Zentralblatt MATH identifier**

1281.91102

**Subjects**

Primary: 91B30: Risk theory, insurance

Secondary: 62P20: Applications to economics [See also 91Bxx] 62P05: Applications to actuarial sciences and financial mathematics

**Keywords**

Characterization theorem insurance premium mean value premium principle additivity consistency iterativity scale invariance

#### Citation

Pratsiovytyi, Mykola; Drozdenko, Vitaliy. Characterization theorems for mean value insurance premium calculation principle. Tbilisi Math. J. 6 (2013), 57--71. doi:10.32513/tbilisi/1528768937. https://projecteuclid.org/euclid.tbilisi/1528768937