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The Central Bank in a certain country is responsible for regulating life insurance companies and deciding how much capital they need to hold on their balance sheets for insurance risks in respect of life insurance policies they sell. Insurance companies receive a fixed premium at the beginning of a new insurance contract but face an uncertain amount of insurance claims over a year. Because of these fixed premiums but uncertain claims, insurance companies need to hold capital to meet future insurance claims. The risk management approach taken by the Central Bank is based on three principles: I. II. III. to set capital requirements based on the age of the insured person the capital required would then be a certain amount per $1 million of life assurance benefit sold for people of that age that the capital to be held by the insurance company should be enough to pay annual insurance claims in 199 out of every 200 years. The Central Bank collects data from six different insurance companies on the amount of life assurance claims they have paid per $1 million of life assurance sold to policyholders of different ages (between 30 and 55) in the last year. (c) Construct R code to produce a simple linear regression model using this data and a scatterplot of the data plus the regression line. The Central Bank sets the capital required at age x for these six insurance companies to be the upper bound of a confidence interval for the response in the simple linear regression model of claims against age. (e) Construct R code to calculate the capital required for these six insurance companies according to principle III above at 251 different ages 30.0, 30.1, 30.2, ..., 54.9, 55.0 as well as the fitted values from your model in part (c) at these ages. Display the capital required and the fitted values by age as lines on the scatterplot of the observed data displaying each line with a different colour.

The Central Bank in a certain country is responsible for regulating life insurance companies and deciding how much capital they need to hold on their balance sheets for insurance risks in respect of life insurance policies they sell. Insurance companies receive a fixed premium at the beginning of a new insurance contract but face an uncertain amount of insurance claims over a year. Because of these fixed premiums but uncertain claims, insurance companies need to hold capital to meet future insurance claims. The risk management approach taken by the Central Bank is based on three principles: I. II. III. to set capital requirements based on the age of the insured person the capital required would then be a certain amount per $1 million of life assurance benefit sold for people of that age that the capital to be held by the insurance company should be enough to pay annual insurance claims in 199 out of every 200 years. The Central Bank collects data from six different insurance companies on the amount of life assurance claims they have paid per $1 million of life assurance sold to policyholders of different ages (between 30 and 55) in the last year. (c) Construct R code to produce a simple linear regression model using this data and a scatterplot of the data plus the regression line. The Central Bank sets the capital required at age x for these six insurance companies to be the upper bound of a confidence interval for the response in the simple linear regression model of claims against age. (e) Construct R code to calculate the capital required for these six insurance companies according to principle III above at 251 different ages 30.0, 30.1, 30.2, ..., 54.9, 55.0 as well as the fitted values from your model in part (c) at these ages. Display the capital required and the fitted values by age as lines on the scatterplot of the observed data displaying each line with a different colour.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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claims age
3367 50
1094 38
766 34
1725 43
2837 48
2844 48
3692 51
594 31
3049 49
3041 49
3078 49
1897 44
5272 55
1587 42
2804 48
1254 40
1170 39
2312 46
4517 53
596 31
4838 54
2784 48
534 30
1167 39
1862 44
2811 48
768 34
1084 38
3674 51
783 34
917 36
653 32
4861 54
3358 50
1420 41
2569 47
3327 50
2052 45
2318 46
1097 38
840 35
834 35
541 30
1737 43
4111 52
1745 43
3319 50
3683 51
5285 55
2818 48
1857 44
592 31
3709 51
2028 45
4538 53
5322 55
1404 41
1192 39
647 32
3335 50
3304 50
533 30
543 30
842 35
1884 44
5298 55
1000 37
602 31
777 34
1186 39
935 36
649 32
4506 53
650 32
785 34
710 33
2290 46
536 30
4150 52
1893 44
922 36
656 32
704 33
540 30
2285 46
1081 38
712 33
4560 53
1164 39
705 33
1880 44
937 36
4475 53
1009 37
850 35
930 36
848 35
1557 42
1175 39
1576 42
1572 42
5223 55
1024 37
1430 41
844 35
2306 46
1866 44
4073 52
1434 41
1086 38
4884 54
1902 44
1281 40
707 33
4464 53
781 34
4160 52
939 36
2778 48
3063 49
1713 43
2014 45
2521 47
599 31
663 32
1410 41
770 34
5248 55
1019 37
2047 45
1721 43
2263 46
2057 45
1424 41
3762 51
1021 37
1181 39
926 36
2545 47
1568 42
4942 54
3092 49
4082 52
4954 54
2033 45
2575 47
1407 41
3107 49
3718 51
1004 37
1102 38
655 32
1275 40
714 33
538 30
1178 39
4896 54
1091 38
2269 46
605 31
3070 49
4850 54
1583 42
5335 55
2581 47
1107 38
1189 39
4121 52
5348 55
1705 43
1251 40
1014 37
4453 53
1266 40
2274 46
4495 53
774 34
719 33
4140 52
661 32
919 36
1561 42
852 35
1437 41
1104 38
659 32
1263 40
546 30
1012 37
4101 52
3034 49
1002 37
603 31
1553 42
5235 55
2533 47
1257 40
2019 45
717 33
598 31
2551 47
1278 40
3744 51
4549 53
3350 50
2527 47
1729 43
721 33
836 35
545 30
3727 51
4908 54
4063 52
3099 49
3288 50
3753 51
928 36
4930 54
2831 48
2557 47
1709 43
3296 50
776 34
1590 42
1741 43
1875 44
2038 45
1269 40
2009 45
1417 41
832 35
591 31
2296 46
2791 48
The Central Bank in a certain country is responsible for regulating life insurance companies and deciding how much capital they need to hold on their balance sheets for insurance risks in respect of life insurance policies they sell. Insurance companies receive a fixed premium at the beginning of a new insurance contract but face an uncertain amount of insurance claims over a year. Because of these fixed premiums but uncertain claims, insurance companies need to hold capital to meet future insurance claims. The risk management approach taken by the Central Bank is based on three principles: 1. II. III. to set capital requirements based on the age of the insured person the capital required would then be a certain amount per $1 million of life assurance benefit sold for people of that age that the capital to be held by the insurance company should be enough to pay annual insurance claims in 199 out of every 200 years. The Central Bank collects data from six different insurance companies on the amount of life assurance claims they have paid per $1 million of life assurance sold to policyholders of different ages (between 30 and 55) in the last year. (c) Construct R code to produce a simple linear regression model using this data and a scatterplot of the data plus the regression line. The Central Bank sets the capital required at age x for these six insurance companies to be the upper bound of a confidence interval for the response in the simple linear regression model of claims against age. (e) Construct R code to calculate the capital required for these six insurance companies according to principle III above at 251 different ages 30.0, 30.1, 30.2, ..., 54.9, 55.0 as well as the fitted values from your model in part (c) at these ages. Display the capital required and the fitted values by age as lines on the scatterplot of the observed data displaying each line with a different colour.
Transcribed Image Text:The Central Bank in a certain country is responsible for regulating life insurance companies and deciding how much capital they need to hold on their balance sheets for insurance risks in respect of life insurance policies they sell. Insurance companies receive a fixed premium at the beginning of a new insurance contract but face an uncertain amount of insurance claims over a year. Because of these fixed premiums but uncertain claims, insurance companies need to hold capital to meet future insurance claims. The risk management approach taken by the Central Bank is based on three principles: 1. II. III. to set capital requirements based on the age of the insured person the capital required would then be a certain amount per $1 million of life assurance benefit sold for people of that age that the capital to be held by the insurance company should be enough to pay annual insurance claims in 199 out of every 200 years. The Central Bank collects data from six different insurance companies on the amount of life assurance claims they have paid per $1 million of life assurance sold to policyholders of different ages (between 30 and 55) in the last year. (c) Construct R code to produce a simple linear regression model using this data and a scatterplot of the data plus the regression line. The Central Bank sets the capital required at age x for these six insurance companies to be the upper bound of a confidence interval for the response in the simple linear regression model of claims against age. (e) Construct R code to calculate the capital required for these six insurance companies according to principle III above at 251 different ages 30.0, 30.1, 30.2, ..., 54.9, 55.0 as well as the fitted values from your model in part (c) at these ages. Display the capital required and the fitted values by age as lines on the scatterplot of the observed data displaying each line with a different colour.
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