CAS Exam 7 Spring 2019, Question 12

Study guide: Exam 7

The Exponential Dispersion Family ("EDF") is a family of distributions with probability density function \pi(y; \theta, \phi) of the form:

\ln \pi(y; \theta, \phi) = \frac{y\theta - b(\theta)}{a(\phi)} + c(y, \phi)

and variance function of the form:

V(\mu) = b''\left((b')^{-1}(\mu)\right)

Part a (0.5 points)

Briefly describe the parameter \theta and the function b(\theta) in the equation above.

Part b (0.5 points)

Explain how the Tweedie sub-family can be obtained from the EDF above.

Part c (0.25 points)

Briefly describe how to select a Tweedie distribution for a heavy-tailed exposure.

Part d (0.75 points)

Given the following information as of December 31, 2018:

Cumulative Paid Loss ($000):

A GLM is used to model the incremental paid losses. The GLM uses a log link function and a Tweedie error distribution specified by:

• p = 1
• b(\theta) = \exp(\theta)
• \mu = \exp(\theta)
• \ln \pi(y; \mu, \phi) = [y \ln \mu - \mu]/\phi

Calculate the accident year 2018 ultimate loss.

Answer this question and see the worked solution

Concepts tested

• Generalized Linear Model
• Tweedie Distribution
• Chain Ladder Method
• Over-Dispersed Poisson Model
• GLM Loss Reserving

More questions from this set

• CAS Exam 7 Spring 2019, Question 11
• CAS Exam 7 Spring 2019, Question 13