CAS Exam 8 Fall 2015, Question 3

Study guide: Exam 8

An actuary is considering using a generalized linear model to estimate the expected frequency of a recently introduced insurance product.

Given the following assumptions:

The expected frequency for a risk is assumed to vary by state and gender.
A log link function is used.
A Poisson error structure is used.
The likelihood function of a Poisson is $l(y;\mu) = \sum \ln f(y_i;\mu_i) = \sum -\mu_i + y_i \ln \mu_i - \ln(y_i!)$
$\beta_1$ is the effect of gender = Male.
$\beta_2$ is the effect of gender = Female.
$\beta_3$ is the effect of State = State A.

Claim Frequency

	State A	State B
Male	0.0920	0.0267
Female	0.1500	0.0500

Given that $\beta_3 = 1.149$ , determine the expected frequency of a male risk in State A.

Part a (2.5 points)