ct010s09a - UNSW ACTL1001 Actuarial Studies and Commerce...

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UNSW ACTL1001 Actuarial Studies and Commerce Sample Solutions Exercises 9 NOTE: the following questions can be computed either by hand or by excel. You should ensure that you are able to use both methods. Exercise 1 Results below 1. To calculate the probability of being on di/erent discount levels for the &fth year we need to raise the transition probability matrix to the power of 5. Firstly the probability of no claims (and moving to the next higher level in a year) is e & 0 : 1 = 0 : 904837 and the probability of one or more claims is 0.095163. The transition matrix will be NCD level 0 1 2 0 0.095163 0.904837 0 1 0.095163 0 0.904837 In Excel we can multiply matrices using the MMULT(,) function. To do this, select an area for the results the size of the resulting matrix ( in this case 3x3). Then enter =mmult(array1, array2) and then press CTRL, SHIFT, ENTER (not just ENTER) and the selected area (3X3) will have the resulting matrix in it. In this case array1 is just the tran- sition matrix and array2 is the same matrix so we multiply the matrix by itself to get the square of the matrix and so on to the 5 th power in this case. The results are given in this case below 1
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Transition matrix Prob of no claims 0.904837 NCD level 0 1 2 0 0.095163 0.904837 0 1 0.095163 0 0.904837 2 0 0.095163 0.904837 Year 2 0.095163 0.086107 0.818731 0.009056 0.172213 0.818731 0.009056 0.086107 0.904837
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ct010s09a - UNSW ACTL1001 Actuarial Studies and Commerce...

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