Unlocking Reserve Assumptions Based on the Retrospective Loss Random Variable

23 Pages Posted: 17 May 2016 Last revised: 28 Aug 2016

See all articles by Jeyaraj Vadiveloo

Jeyaraj Vadiveloo

Willis Towers Watson

Gao Niu

University of Connecticut - Department of Mathematics

Emiliano A. Valdez

University of Connecticut - Department of Mathematics

Guojun Gan

University of Connecticut

Date Written: May 14, 2016

Abstract

In this paper, we define a retrospective loss random variable and mathematically demonstrate that its expectation is the retrospective reserve which in turn is equivalent to the prospective reserve. By defining an associated random variable for the retrospective reserve, similar to the prospective loss random variable for the prospective reserve, we can further explore and understand various properties of this retrospective loss random variable. In particular, we find and demonstrate that this retrospective random variable can be a powerful tool for providing us valuable historical information on the pattern and significance of deviation of actual experience from that assumed for reserving purposes. This valuable information can subsequently guide us as to whether it becomes necessary to adjust prospective reserves and the procedure to do so. The paper concludes with a model of a block of in force policies with actual experience different from reserving assumptions, and a rigorous and consistent methodology on how prospective reserves could be adjusted based on the realized retrospective loss random variable.

Keywords: Life Insurance Reserves, Prospective and Retrospective Loss Random Variables, Emerging Mortality Experience, Unlocking Assumptions

JEL Classification: G22, A10

Suggested Citation

Vadiveloo, Jeyaraj and Niu, Gao and Valdez, Emiliano A. and Gan, Guojun, Unlocking Reserve Assumptions Based on the Retrospective Loss Random Variable (May 14, 2016). Available at SSRN: https://ssrn.com/abstract=2779947 or http://dx.doi.org/10.2139/ssrn.2779947

Jeyaraj Vadiveloo

Willis Towers Watson ( email )

875 Third Avenue
New York, NY 10022
United States

Gao Niu

University of Connecticut - Department of Mathematics ( email )

196 Auditorium Rd U-3009
Storrs, CT 06269-3009
United States

Emiliano A. Valdez (Contact Author)

University of Connecticut - Department of Mathematics ( email )

341 Mansfield Road U-1009
Storrs, CT 06269-1009
United States

HOME PAGE: http://www.math.uconn.edu/~valdez

Guojun Gan

University of Connecticut ( email )

341 Mansfield Rd, U-1009
Storrs, CT 06269-1009
United States

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