On Unbalanced Data and Common Shock Models in Stochastic Loss Reserving

29 Pages Posted: 23 Dec 2018

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

Phuong Anh Vu

UNSW Business School - School of Risk and Actuarial Studies; Université de Montréal - Département de mathématiques et de statistique

Bernard Wong

UNSW Australia Business School, School of Risk & Actuarial Studies

Date Written: December 22, 2018

Abstract

Introducing common shocks is a popular dependence modelling approach, with some recent applications in loss reserving. The main advantage of this approach is the ability to capture structural dependence coming from known relationships. In addition, it helps with the parsimonious construction of correlation matrices of large dimensions. However, complications arise in the presence of "unbalanced data", that is, when (expected) magnitude of observations over a single triangle, or between triangles, can vary substantially. Specifically, if a single common shock is applied to all of these cells, it can contribute insignificantly to the larger values and/or swamp the smaller ones, unless careful adjustments are made. This problem is further complicated in applications involving negative claim amounts. In this paper, we address this problem in the loss reserving context and illustrate it using a common shock Tweedie model. We show that the solution not only provides a much better balance of the common shock proportions relative to the unbalanced data, but it is also parsimonious. Finally, the common shock Tweedie model also provides distributional tractability.

Keywords: Stochastic loss reserving, Dependence, Common shock, Unbalanced data, Negative claims, Multivariate Tweedie distribution, Bayesian estimation

JEL Classification: G22

Suggested Citation

Avanzi, Benjamin and Taylor, Greg and Vu, Phuong Anh and Wong, Bernard, On Unbalanced Data and Common Shock Models in Stochastic Loss Reserving (December 22, 2018). UNSW Business School Research Paper No. 2018ACTL01. Available at SSRN: https://ssrn.com/abstract=3303255 or http://dx.doi.org/10.2139/ssrn.3303255

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)

Phuong Anh Vu (Contact Author)

UNSW Business School - School of Risk and Actuarial Studies ( email )

Sydney, NSW 2052
Australia

Université de Montréal - Département de mathématiques et de statistique ( email )

Montreal, Quebec H3C 3J7
Canada

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

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