On Some Multivariate Sarmanov Mixed Erlang Reinsurance Risks: Aggregation and Capital Allocation

20 Pages Posted: 14 Nov 2016

See all articles by Gildas Ratovomirija

Gildas Ratovomirija

University of Lausanne

Maissa Tamraz

Universite de Lausanne; Nankai University

Raluca Vernic

Ovidius University of Constanta

Date Written: November 13, 2016

Abstract

Following some recent works on risk aggregation and capital allocation for mixed Erlang risks joined by Sarmanov's multivariate distribution, in this paper we present some closed-form formulas for the same topic by considering, however, a different kernel function for Sarmanov's distribution, not previously studied in this context. The risk aggregation and capital allocation formulas are derived and numerically illustrated in the general framework of stop-loss reinsurance, and then in the particular case with no stop-loss reinsurance. A discussion of the dependency structure of the considered distribution, based on Pearson's correlation coefficient, is also presented for different kernel functions and illustrated in the bivariate case.

Keywords: Sarmanov distribution, Mixed Erlang distribution, Capital allocation, Risk aggregation, Stop-loss reinsurance, Dependency

JEL Classification: C46, G22

Suggested Citation

Ratovomirija, Gildas and Tamraz, Maissa and Vernic, Raluca, On Some Multivariate Sarmanov Mixed Erlang Reinsurance Risks: Aggregation and Capital Allocation (November 13, 2016). Available at SSRN: https://ssrn.com/abstract=2868638 or http://dx.doi.org/10.2139/ssrn.2868638

Gildas Ratovomirija

University of Lausanne ( email )

Unil-Dorigny
Vaud
Lausanne, Vaud 1015
Switzerland

Maissa Tamraz

Universite de Lausanne ( email )

Quartier Chambronne
Lausanne, 1015
Switzerland

Nankai University

94 Weijin Road
Tianjin, 300071
China

Raluca Vernic (Contact Author)

Ovidius University of Constanta ( email )

b-dul Mamaia nr. 124
Constanta, 900527
Romania

Register to save articles to
your library

Register

Paper statistics

Downloads
5
Abstract Views
179
PlumX Metrics