Contingencies in insurance and pensions ETC3530
"Age""lx" 010000 19998.14459420364 29996.11487066137 39993.89449262133 49991.46560028809 59988.80867041251 69985.90236324979 79982.7233558118 89979.24616026088 99975.44292621092 109971.28322561693 119966.73381884871 129961.75840045731 139956.31732305676 149950.36729765989 159943.86106872749 169936.74706211761 179928.96900406033 189920.46550923626 199911.16963600953 209901.00840686584 219889.90229213827 229877.76465518022 239864.50115727473 249850.00912076738 259834.17684919111 269816.88290353497 279797.99533431654 289777.37086977665 299754.85406135473 309730.27638865965 319703.45532746526 329674.19338587874 339642.27711580717 349607.47610924401 359569.54199177906 369528.2074291783 379483.18516696365 389434.16712773274 399380.82359658466 409322.80253154689 419259.72904341576 429191.20509799909 439116.8095034371 449036.09825609348 458948.60533042174 468853.84401112015 478751.30887959215 488640.47858089857 498520.81951152308 508391.7905816536 518252.8492173201 528103.45877629562 537943.09755544079 547771.26956396494 557587.51722419035 567391.43613558739 577182.69199530237 586961.03970484514 596726.34460342843 606478.60564898731 616217.98021388096 625944.80997046429 635659.64711086306 645363.27987732346 655056.75608105492 664741.40297160347 674418.84150686022 684090.99279726883 693760.07429939621 703428.58326796585 713099.26510565678 722775.06464565508 732459.05912947324 742154.37275294551 751864.07416526417 761591.06018534069 771337.931138402 781106.86541370506 79899.50280359598 80716.847521864799 81559.202088734904 82426.142115101789 83316.539160495625 84228.634276261949 85160.158941161945 86108.493628818427 8770.848352238938 8844.4455154878266 8926.6844215008692 9015.2694620984247 918.29012657501616 924.24932981009783 932.04526476080808 940.918914137853561 950.382895961568843 960.146921750746825 970.0515133440430285 980.0163641396676348 990.00466627698362067 1000 1010 1020 1030 ETC3530 Contingencies in Insurance and Pensions Assignment 1 Due date: August 30, 2020 Sensitivity analysis – Focus on interest rate Objective: The objective of this assignment is to study the effect of interest rate on the expected present value of two insurance products, where the mortality table is fixed. The two products are whole life annuities payable in arrears, with expected present value given by: ax = ∑ k≥1 vk kpx, and whole life assurances, with expected present value given by: Ax = ∑ k≥0 vk+1 k|qx, where v = 11+i , and i is the interest rate. Questions: A. Using the software R, calculate the values of ax and Ax in function of the interest rate i, with i = 0%, 1%, 2%, ..., 50%, for the ages x = 0, 30 and 60. The results must be provided in one graph where the interest rate is on the X-axis. Ensure that the X and Y axes of the graph are properly labeled, and include a clear legend to distinguish the different curves. For a proper comparison, standardise each curve by the corresponding value for i = 0%. This will allow to determine the increase/decrease per-unit of EPV of the product with i = 0%. More specifically, the figures should display ax@iax@0% and Ax@i Ax@0% , for different values of x, in function of the interest rate i. B. Comment on the results regarding the sensitivity of each product with respect to the interest rate for each age. ETC3530 - Assignment 1 - Page 2 of 3 Instructions: 1. Download the mortality table using your student ID number on the following link: https://hamzahanbali.shinyapps.io/mortalitytables/ 2. Use the function read.table() to import the mortality table in R, as follows: read.table(‘Your File Directory/STUDENTID.txt’,dec=‘.’,sep=‘\t’,header=TRUE) 3. Submit the following documents: • the results in the form of a PDF file, not exceeding 2 pages, including the graph – keep it concise! • the R code. Do not forget to add some comments explaining the code, • a ‘.txt’ file containing the output of the analysis (i.e. ax@iax@0% and Ax@i Ax@0% , for each age), as shown in the figure below. Use the function colnames() to name the columns of the output matrix following the order shown in the figure below, as well as the function write.table() to export the results. Include the following commands in this function: (a) sep=‘\t’ for the columns in the ‘.txt’ file to be tab-separated. (b) dec=‘.’ to specify the dot as symbol for the decimals, (c) rown.names=FALSE to suppress the default first column created by the function. (d) the name of the ‘.txt’ file must be your student ID number. Assuming your matrix of output is named Output, here is an example of the R code to export the results: write.table(Output,‘File directory/STUDENTID.txt’,sep=‘\t’,dec=‘.’,row.names=FALSE) • Here is an example of the expected ‘.txt’ output: https://hamzahanbali.shinyapps.io/mortalitytables/ ETC3530 - Assignment 1 - Page 3 of 3 Question Points Max A 60 B 40 Total 100