Stochastic Loss Reserving with Dependence: A Flexible Multivariate Tweedie Approach

27 Pages Posted: 4 Apr 2016 Last revised: 14 Jul 2016

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: March 30, 2016

Abstract

Stochastic loss reserving with dependence has received increased attention in the last decade. A number of parametric multivariate approaches have been developed to capture dependence between lines of business within an insurer's portfolio. Motivated by the richness of the Tweedie family of distributions, we propose a multivariate Tweedie approach to capture cell-wise dependence in loss reserving. This approach provides a transparent introduction of dependence through a common shock structure. In addition, it also has a number of ideal properties, including marginal flexibility, transparency, and tractability including moments that can be obtained in closed form. Theoretical results are illustrated using a simulated data set and a real data set from a property-casualty insurer in the US.

Keywords: Stochastic Loss Reserving, Dependence, Multivariate Tweedie Distribution, Common Shock, Bayesian Estimation

JEL Classification: G22

Suggested Citation

Avanzi, Benjamin and Taylor, Greg and Vu, Phuong Anh and Wong, Bernard, Stochastic Loss Reserving with Dependence: A Flexible Multivariate Tweedie Approach (March 30, 2016). UNSW Business School Research Paper No. 2016ACTL01. Available at SSRN: https://ssrn.com/abstract=2753540 or http://dx.doi.org/10.2139/ssrn.2753540

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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