One-year premium risk and emergence pattern of ultimate loss based on conditional distribution

ASTIN Bulletin: The Journal of the IAA, Volume 50, Issue 2, May 2020, pp. 479 - 511, DOI: https://doi.org/10.1017/asb.2020.10

33 Pages Posted: 17 Apr 2020 Last revised: 21 Sep 2021

See all articles by Lukasz Delong

Lukasz Delong

Warsaw School of Economics (SGH) - Institute of Econometrics

Marcin Szatkowski

Warsaw School of Economics (SGH) - Institute of Econometrics; STU ERGO Hestia SA

Date Written: May 5, 2020

Abstract

We study the relation between one-year premium risk and ultimate premium risk. In practice, the one-year risk is sometimes related to the ultimate risk by using a so-called emergence pattern formula which postulates a linear relation between both risks. We define the true emergence pattern of the ultimate loss for the one-year premium risk based on a conditional distribution of the ultimate loss derived from a multivariate distribution of the claims development process. We investigate three models commonly used in claims reserving and prove that the true emergence pattern formulas are different from the linear emergence pattern formula used in practice. We show that the one-year risk, when measured by VaR, can be under and overestimated if the linear emergence pattern formula is applied. We present two modifications of the linear emergence pattern formula. These modifications allow us to go beyond the claims development models investigated in the first part and work with an arbitrary distribution of the ultimate loss.

Keywords: One-year risk, ultimate risk, emergence pattern, Solvency II, claims development process

JEL Classification: G22

Suggested Citation

Delong, Lukasz and Szatkowski, Marcin, One-year premium risk and emergence pattern of ultimate loss based on conditional distribution (May 5, 2020). ASTIN Bulletin: The Journal of the IAA, Volume 50, Issue 2, May 2020, pp. 479 - 511, DOI: https://doi.org/10.1017/asb.2020.10, Available at SSRN: https://ssrn.com/abstract=3559808 or http://dx.doi.org/10.2139/ssrn.3559808

Lukasz Delong (Contact Author)

Warsaw School of Economics (SGH) - Institute of Econometrics ( email )

Niepodleglosci 164
Warsaw, 02-554
Poland

Marcin Szatkowski

Warsaw School of Economics (SGH) - Institute of Econometrics ( email )

Niepodleglosci 164
Warsaw, 02-554
Poland

STU ERGO Hestia SA ( email )

ul. Hestii 1
Sopot, 81-731
Poland

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
45
Abstract Views
284
PlumX Metrics