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(Created page with "'''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 display = "block"> \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...") |
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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 | 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 display = "block"> \mu = 95000 * (1-F^{-1})^{-1}</math> | <math display = "block"> \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. | 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. The expected ultimate loss equals 95,000 * (1-1/1.4314) = 315,213.3. | ||
Latest revision as of 23:15, 24 October 2024
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. The expected ultimate loss equals 95,000 * (1-1/1.4314) = 315,213.3.