Financial Risk Manager Part 1

Financial Risk Manager Part 1

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On Tuesday, an insurance company receives a total of 10 claims for automobile policies. After the first-round assessment, it's found that the mean claim amount of the 10 claims is 426whilethestandarddeviationis112.OnTuesday,thechiefclaimsanalystauthorizestheremovalofoneoftheclaimsfor426 while the standard deviation is 112. On Tuesday, the chief claims analyst authorizes the removal of one of the claims for 545 from the list on grounds that it's fraught with fraud. Compute the standard deviation for the remaining set of 9 claims.

TTanishq

Explanation:

Calculation Steps

Step 1: Calculate the total sum of original claims

  • Mean = $426, n = 10
  • Total sum ∑x = 426 × 10 = 4,260

Step 2: Calculate new total after removing fraudulent claim

  • Remove claim of $545
  • New ∑x = 4,260 - 545 = 3,715
  • New mean = 3,715 ÷ 9 = $412.8

Step 3: Calculate sum of squares for original claims

Using the formula: s² = 1/(n-1)[∑x² - n·x̄²]

  • 112² = 1/9[∑x² - 10 × 426²]
  • 12,544 = 1/9[∑x² - 1,814,760]
  • ∑x² = 12,544 × 9 + 1,814,760 = 1,927,656

Step 4: Calculate sum of squares after removing fraudulent claim

  • Remove 545² = 297,025
  • New ∑x² = 1,927,656 - 297,025 = 1,630,631

Step 5: Calculate variance for remaining 9 claims

  • s² = 1/(9-1)[1,630,631 - 9 × 412.8²]
  • s² = 1/8[1,630,631 - 9 × 170,403.84]
  • s² = 1/8[1,630,631 - 1,533,634.56]
  • s² = 1/8 × 96,996.44 = 12,124.555

Step 6: Calculate standard deviation

  • s = √12,124.555 ≈ 110.2

Therefore, the standard deviation for the remaining 9 claims is approximately $110.2

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