Q4 - to only half year as the PV of the continuous case, as...

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Q4 (i) Calculate the Gross future loss We know Loss=PV(Benefit)+expense-PV(premium) Let y=min(K+1,65-x) B be the benefit payment For the simple bonus policy The present value of the premium : y The present value of the expense : 250+150*v^(Tx)+2%*( äy -1) The present value of the benefit: B*(1+6%*K)*v^(Tx) So the future loss is [B*(1+6%*K)+150]*v^(Tx)+250-P(0.98( äy +2% ) For the compound bonus policy The present value of the benefit : B(1.04)^(K)*v^(Tx) The other is the same So the future loss is [B(1.04)^(K)+150]*v^(Tx)+250- P(0.98( äy +2% ) (ii) To get the premium For simple bonus policy Pä[40]:25 -(250+150Ã[40]+0.02P(ä[40]:25 -1 ))=6%*200000(IÃ)[40]+188000 Ã[40] Premiums Expense Benefits Since Ã[40]≈(1+4%)^(0.5)*À[40] In order to calculate the continuous case, we can approximate it by using discrete case accumulate
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Unformatted text preview: to only half year as the PV of the continuous case, as also used in the CT5 notes . 15.887P-(250+150*1.04^(0.5)*0.23041+0.02P(15.887-1)) =1.04^(0.5)[12000(I[40]+188000 [40])] 15.887P=141566.40+285.25+0.298P P=9099.5 For the compound bonus policy The expected present value of the benefit =200000[v^(0.5)q[40]+v^(1.5)*(1.04)*1|q[40]+v^(2.5)*(1.04)^2*2|q[40]+)] =200000/1.04^(0.5)*[q[40]+1|q[40]+2|q[40]+. .] =200000/1.04^(0.5) =196116.14 (iii) For the net premium reserve First we should compute the net premium Pnet*40:25 =200000 40 Pnet=200000*1.04^(0.5)*0.23056/15.884=2960.54 Then using the net premium, we can get the net premium reserve at year 10 10 V=290000 50-Pnet 50:15 =290000*1.04^(0.5)*0.32907-2960.54*11.253=64005...
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This note was uploaded on 06/12/2011 for the course ASB 1001,2522, taught by Professor Nicole during the One '09 term at University of New South Wales.

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