You are given the following information:

1. Reported claims = 255,000
2. IBNR using Bornhuetter-Ferguson method = 95,000
3. IBNR using the chain ladder method = 110,000

Calculate the expected ultimate loss.

• 285,000
• 300,000
• 315,000
• 350,000
• 365,000

Solution: C

The IBNR using the Bornhuetter-Ferguson method equals [math]\mu (1-F^{-1}) [/math] where [math]\mu[/math] is the expected ultimate loss and [math]F[/math] is the development factor. Hence the expected loss equals

[[math]] \mu = 95000 * (1-F^{-1})^{-1}[[/math]]

To find the development factor, we know that the IBNR using the chain ladder method equals 110,000 = 255,000 * ([math]F[/math]-1) which implies that [math]F[/math] equals 1.4314. Since [math]C[/math] equals 255,000 then the estimated loss equals 95,000 * (1-1/1.4314) = 315,213.3.