Finite Mixed Erlang Distribution: Moment-Based Approximation and Loss Modeling with Actuarial Applications

• Activity Number: 442
• Type: Topic Contributed
• Date/Time: Wednesday, August 6, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Hélène Cossette*+ and Etienne Marceau and David Landriault and Khouzeima Moutanabbir
• Companies: Université Laval and Université Laval and University of Waterloo and American University in Cairo
• Keywords: Mixed Erlang distribution ; Moment-based approximation ; Loss distribution

Abstract

In this talk, we assume that a financial entity is subject to a risk X which has known moments, but for which its distribution function is unknown or does not admit a tractable closed-form expression. Based on the recent advances on the mixed Erlang class of distributions, we propose to approximate its distribution function by a member of this class using a moment-matching method. This approximation is mathematically justified and offers a greater level of flexibility. In addition, risk measures such as Value-at-Risk (VaR), tail-Value-at-Risk (TVaR) and stop-loss premium are readily available for any member of the mixed Erlang class which will be of great use to insurers. In the talk, we provide the theoretical ground of the proposed approximation. This approximation method can also be viewed as a moment-matching estimation method for the loss distribution of a given risk X. This will be illustrated with an example based on catastrophe risk data.