Exam April 2005 Q7(iii)

Discussion in 'ST3' started by f888bet, Mar 22, 2009.

  1. f888bet

    f888bet Member

    I'm struggling to follow the solution to this question. I understand how you get to R = 0.02 * Theta, and I also understand how
    Capital = 115.12 / Theta. However, I don't the next bit of the solution.

    Where does the bit

    Theta = 10% * Capital / 10m, and the following

    Theta^2 = 115.13m / 100m term come from?

    This makes absolutely no sense to me - Anyone understand this?
     
  2. You're happy that Capital = 115.13m/theta.

    If we now think about the Return on capital (or profit) for Company A, we notice that:

    Return on capital * Capital = theta * Expected claims

    since theta is the security loading i.e. the extra amount loaded onto the premiums to represent the profit.

    We know that the Expected claims = 10m (the loss cost for A)
    We also know that the required Return on capital = 10%
    so:
    10% * Capital = theta * 10m
    and so
    Capital = (10m * theta) / 10%

    Equating this with the fact that Capital = 115.13m/theta from above gives the result that
    theta^2 = 115.13/100m
     

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