- Level: University Degree
- Subject: Miscellaneous
- Word count: 3432
Actuarial Studies - Investment Policy and Calculation of Profit and Loss
Extracts from this document...
Introduction
CONTENTS INTRODUCTION ....................................................................... 3 DETERMINATION OF PREMIUM & CAPITAL ........................ 4 I. ESTIMATION OF CLAIM ........................................................ 4 II. CALCULATION OF PREMIUM ............................................... 4 III. CALCULATION OF CAPITAL .................................................. 5 INVESTMENT POLICY I. ASSET MODEL ........................................................................ 6 II. INVESTMENT STRATEGY ....................................................... 6 PROFIT OR LOSS ANALYSIS .................................................... 7 CONCLUSION ........................................................................... 8 RECOMMENDATION ............................................................... 8 APPENDIX ................................................................................ 9 INTRODUCTION This report intends to summarise the findings of the new commencement of the flood insurance product that proposes to be renewed annually for a period of three years. Within this time horizon, all of the surplus and premiums less claims collected are reinvested in either zero coupon bonds or the stock market; which believed to follow similar movement to the share prices of AMP Limited (AMP). However at any time when the funds go insolvent, then all future cash flows are cancelled. This report aims to provide the essential information regarding this innovative flood insurance policy, which include: * The premium charged for the flood insurance product every year. * The amount of the capital needed to be contributed by the shareholders in the beginning of this policy. * Make selection for the most favourable investment policy between stocks or zero coupon bonds, with the surplus of premiums over claims. Furthermore, this report will also present the integral information on the * Profit and Loss Distribution of this policy at the end of the third year * Expected Value and Variance of the Profit or Loss * Probability of Loss * Expected Value of Loss, if a loss occurs ("Excepted Shortfall") DETERMINATION OF PREMIUM AND CAPITAL In order to calculate the level of premium and capital, it is essential to firstly, consider the amount of expected amount of aggregate claim. I. Estimation of claim Since this insurance policy provides cover for flood risks, the aggregate claim amount is assumed to follow a "compound Poisson" model. The total amount of aggregate claim in year t can be expressed as: Where N(t) ...read more.
Middle
1/2 ln(20000) = -1/2 ln(e?^2 - 1) ln(20000)-1 = ln(e?^2 - 1) 20000-1 = e?^2 - 1 1 + 20000-1 = e?^2 ln(1 + 20000-1) = ?^2 ? = [ln(1 + 20000-1)] 1/2 ? = 7.070979426 ? 10-3 ............................................( sub ( into ( ? = 9.903462553 ? Reasoning for expected aggregate claim Denote the number of claims by N(t) and the loss distribution for the ith claim by X(i,t) for i = 1,2,3,...,N(t). The number of claims that occurs takes the values N(t) = n(t). Moreover the total claim payments (aggregate loss) is denoted by S. The aggregate loss is the sum of all claim amounts that occur during the policy year. Accordingly S = X(1,t) + X(2,t) + X(3,t) + ... + X(N(t)) = The expected claims cost will be the expected value of the aggregate claims such that E[S] = To evaluate this probability, conditional probability is utilised. This means the different number of possible claims that will occur and the probability that these numbers of claims occur, so the expected aggregate loss is E[S] = With the losses being independent of the number of claims and each loss X(i,t) has the same probability density �x (x) then = E[X| N(t) = n(t)] = [xi] �x (x) dx = E[Xi] = n E[X] Therefore E[S] = n E[X] Pr[N(t) = n(t)] = E[n(t)] E[X] Since the average number of claims are 4.5, thus E[n(t)] = 4.5 and E[X] = 20000 ?E[S] = Expected aggregate claim = 4.5 ? 20000 = $90 0008 ? Claims This is how the spreadsheet should be set out like producing 7000 simulations each year: Table 1: Claim Data A B C D E 11 Number of claims Random Number Amount claimed Aggregate claim Rounded Aggregate Claim 12 0 0.426314 19973.2469 19973.2469 20000 13 2 0.399829 19963.6425 39927.2850 40000 14 1 0.18769 19874.5340 79498.1362 80000 15 5 0.31489 19931.4486 59794.3489 60000 ... ...read more.
Conclusion
of claim Aggregate claim (AC) Stock(3) ZCB(3) A(3) v(w) v(w)*1/7000 E[profit] 9 5 99725.15 43770.04 123597.1 67641.94 -1E-147 -1.8719E-151 $64,049.87 10 1 19950.41 60030.19 167638.8 207718.6 0 0 $124,351.76 11 2 39940.64 61744.09 214093.7 235897.1 0 0 $172,520.54 12 7 138502.9 62302.28 145376.6 69175.92 -6E-151 -8.7357E-155 $104,361.60 13 2 39844.51 0 0 0 -1 -0.000142857 -$30,927.47 14 4 80314.93 0 0 0 -1 -0.000142857 -$33,560.22 15 3 60410.67 50946.58 192404.4 182940.3 0 0 $140,033.74 16 2 39817.65 37625.03 183702.5 181509.9 0 0 $118,010.28 17 7 140088.6 40521.57 116755.3 17188.3 -4.7E-38 -6.77614E-42 $53,959.67 18 3 59483.43 0 0 0 -1 -0.000142857 -$16,046.45 ... ... ... ... ... ... ... ... 7009 Ave. claim 90655.96 U(w) -0.295084598 Ave. E[profit] = 72 448.03 If the company makes a negative profit, the asset at the end of the year will be written off to zero. However, positive assets are rounded off to the nearest 10,000s for the purpose of the evaluation of profit or loss distribution. Excel function for column A(3): if(stock(3)+ZCB(3)-AC>=0, stock(3)+ZCB(3)-AC,0) These groups are tabulated and tallied before the distribution graph is plotted, Refer to graph 2. The variant of the profit or loss distribution can be calculated using the variant formula. Var[X] = E[(X - E[X])2] To do this by excel, one extra column is created for the calculation of (X - E[X])2(1/7000) where 1/7000 is the probability for each value of x. In this case x is the value of profits and E[X] is the average of the profits. The sum of this column will give the variance of the profits, which equals to 6,319,587,035. The formula used is SUM(). 1 See appendix for the calculation of ? and ?. 2 See appendix for reasoning of the expected aggregate claim 3 See appendix on the sample excel format 4 See calculation for Capital 5 Calculation of ? using the least squared technique 6 Investment Return and Expected Utility 7 Details on excel functions, calculation on expected value and variance. 8 Pg 196 - 197, Michael Sherris, (2009), Principles of Actuarial Science, McGraw Hill ?? ?? ?? ?? 14 --- -2- ...read more.
This student written piece of work is one of many that can be found in our University Degree Miscellaneous section.
Found what you're looking for?
- Start learning 29% faster today
- 150,000+ documents available
- Just £6.99 a month