Matrix calculation for ultimate and one-year risk in the semi-markov individual loss reserving model

Abstract

This paper proposes a multistate model with a Semi-Markov dependence structure describing the different stages in the settlement process of individual claims in general insurance. Every trajectory, from reporting to closure is combined with a modeling of individual link ratios to obtain the ultimate cost of each claim. Analytical expressions are derived for the moments of ultimate amounts whereas quantile risk measures can be obtained by simulation. In the one-year view, the proposed matrix calculations avoid the simulation-within-simulation issue and offer a tractable evaluation method. A case study illustrates the relevance of the proposed approach.

Sector: Insurance

Authors: Carole Bettonville,

Louise D’Oultremont,  Michel Denuit

and Julien Trufin 

Publisher: Scandinavian

Actuarial Journal

Date: November 2020

Language: English

About the authors

Carole_rond

Carole Bettonville

Carole is a Freelance Expert at Detralytics. During her various missions, Carole has worked on various fields such as calibration of lapse rate and mortality models and a project as part of the IFRS 17 framework, aiming at identifying a Best Estimate allocation key based on some claims characteristics. Prior to joining Detralytics, Carole worked as an intern at Axa Belgium. 

Louise_rond

Louise D'Oultremont

Louise is People Lead and part of the Talent Consolidation Program (TCP). Prior to joining Detralytics, Louise did an internship at Axa Belgium, where she was in the risk pricing team. After a few years at Detralytics, Louise developed a solid knowledge in actuarial sciences. In particular, she worked on pricing and reserving in the fields of non-life and health insurance.

Michel Denuit

Michel is an Honorary Scientific Advisor at Detralytics, as well as a professor in actuarial science at the Université Catholique de Louvain. He has international experience as a visiting professor, and has promoted many projects in collaboration with the industry. At Detralytics, Michel coaches young talents, provides cutting-edge training, fosters innovation and oversees R&D projects.

Julien Trufin

Julien is a Scientific Advisor at Detralytics, as well as a professor in Actuarial Science at the department of mathematics of the Université Libre de Bruxelles. Julien has experience as a consultant and a strong academic background developed at prominent institutions, including Université Laval (Canada), UCL, and ULB (Belgium). At Detralytics, Julien coaches young talents, provide cutting-edge training, fosters innovation and oversees R&D projects.

Share This Post

More To Explore

Do You Want To Boost Your Business?

drop us a Message and keep in touch