A Multivariate Micro-Level Insurance Counts Model With a Cox Process Approach

24 Pages Posted: 4 Apr 2019

See all articles by Benjamin Avanzi

Benjamin Avanzi

UNSW Australia Business School, School of Risk and Actuarial Studies

Greg Taylor

UNSW Australia Business School, School of Risk & Actuarial Studies

Bernard Wong

UNSW Australia Business School, School of Risk & Actuarial Studies

Xinda Yang

University of New South Wales (UNSW) - School of Actuarial Studies

Date Written: March 18, 2019

Abstract

When calculating the risk margins of a company with multiple Lines of Business–typically, a quantile in the right tail of an aggregate loss, assumptions about the dependence structure between the different Lines are crucial. Many current multivariate reserving methodologies focus on aggregated claims information, typically in the format of claim triangles. This aggregation is subject to some inefficiencies, such as possibly insufficient data points, and potential elimination of useful information. This inefficiency is particularly problematic for the estimation of dependence. So-called 'micro-level models', on the other hand, utilise more granular levels of observations. Such granular data lend themselves naturally to a stochastic process modelling approach. However, the literature interested in the incorporation of a dependency structure with a micro-level approach is still scarce.

In this paper, we extend the literature of micro-level stochastic reserving models to the multivariate context. We develop a multivariate Cox process to model the joint arrival process of insurance claims in multiple Lines of Business. This allows for a dependency structure between the frequencies of claims. We also explicitly incorporate known covariates, such as seasonality patterns and trends, which may explain some of the relationship between two insurance processes (or at least help tease out those relationships). We develop a filtering algorithm to estimate the unobservable stochastic intensities. Model calibration is illustrated using real data from the AUSI data set.

Keywords: Dependency modelling, Cox process, Shot noise, Insurance claims counts, Micro-level model, Markov chain Monte Carlo

JEL Classification: C51, C53, C55, G22

Suggested Citation

Avanzi, Benjamin and Taylor, Greg and Wong, Bernard and Yang, Xinda, A Multivariate Micro-Level Insurance Counts Model With a Cox Process Approach (March 18, 2019). UNSW Business School Research Paper No. 2019ACTL02. Available at SSRN: https://ssrn.com/abstract=3354434 or http://dx.doi.org/10.2139/ssrn.3354434

Benjamin Avanzi

UNSW Australia Business School, School of Risk and Actuarial Studies ( email )

UNSW Sydney, NSW 2052
Australia

Greg Taylor

UNSW Australia Business School, School of Risk & Actuarial Studies ( email )

Level 6, East Lobby
UNSW Business School Building, UNSW
Sydney, NSW 2052
Australia
+61 421 338 448 (Phone)

Bernard Wong

UNSW Australia Business School, School of Risk & Actuarial Studies ( email )

Room 2058 South Wing 2nd Floor
Quadrangle building, Kensington Campus
Sydney, NSW 2052
Australia

Xinda Yang (Contact Author)

University of New South Wales (UNSW) - School of Actuarial Studies ( email )

Sydney, NSW 2052
Australia

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