Probability Models Generated via Line Integral and Joint Life Insurance Application


  • Nikolai Kolev



Characterization, Functional equation, Hazard gradient vector, Line integral


We construct via line integral and characterize a class of bivariate continuous distributions with a multiplicative representation of the sum of hazard gradient components. The corresponding joint survival function is a solution of functional equation allowing to generate new members of the class. We apply a particular member to it a big Canadian joint life insurance data set improving the inference and conclusions made by of another authors.


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Biografia do Autor

Nikolai Kolev

IME-USP, São Paulo, SP


Fabio Gobbi, Nikolai Kolev, and Sabrina Mulinacci. Joint life insurance pricing using extended Marshall-lkin models. In: ASTIN Bulletin: The Journal of the IAA 49.2 (2019), pp. 409-432. doi: 10.1017/asb.2019.3.

Nikolai Kolev. Characterizations of the class of bivariate Gompertz distributions. In: Journal of Multivariate Analysis 148 (2016), pp. 173-179. doi:10.1016/j.jmva.2016.03.004.

Nikolai Kolev. Discrete line integral on uniform grids: Probabilistic interpretation and applications. In: Brazilian Journal of Probability and Statistics 34.4 (2020), pp. 821-843. doi: 10.1214/19-BJPS454.

H. V. Kulkarni. Characterizations and Modelling of Multivariate Lack of Memory Property. In: Metrika 64.2 (2006), pp. 167-180. doi: 10.1007/s00184-006-0042-2.

Albert W. Marshall. Some comments on the hazard gradient. In: Stochastic Processes and their Applications 3.3 (1975), pp. 293-300. doi: 10.1016/0304-4149(75)90028-9.

Jayme Pinto and Nikolai Kolev. Sibuya-type bivariate lack of memory property. In: Journal of Multivariate Analysis 134 (2015), pp. 119-128. doi: 10.1016/j.jmva.2014.11.001.

Prasanna K. Sahoo and Palaniappan Kannappan. Introduction to Functional Equations. Chapman and Hall/CRC, Feb. 2011. doi: 10.1201/b10722.






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