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MATH 3640 – Assignment
Creation date：2024-06-14 17:21:14
Belonging category：数学mathematics
Assignment

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MATH 3640 – Assignment 

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1) (1.5 points) Given an annual premium trend of 10%, using one-step trending, what factor
should be applied to project Calendar Year 2022 Earned Premiums, assuming semi-annual
policies with a proposed rate effective date of 1/1/2025, where rates are expected to be in effect
for 2 years?
2) (1.75 points) Given an annual premium trend of 5%, using one-step trending, what factor
should be applied to project Policy Year 2022 Earned Premiums, assuming semi-annual policies
with a proposed rate effective date of 1/1/2025, where rates are expected to be in effect for 3
years?
3) (4.25 points) Given the following information, use two-step trending to calculate EPAPR at
prospective levels in total, for all historical years given:
 Semi-annual policies, written uniformly throughout the year
 Projected premium trend = 8%
 Proposed rate effective date is 7/1/2025
 Rates will be in effect for 1.5 years
Calendar Year EPAPR Avg EPAPR Avg On-Leveled WP
2020 5,000,000 4,900 5,000
2021 5,100,500 5,050 5,050
2022 5,500,000 5,150 5,100
2023 5,900,000 5,850 6,000
4) (5.5 points) Given the following information, use two-step trending to calculate EPAPR at
prospective levels in total, for all historical periods given:
 Semi-annual policies, written uniformly throughout the year
 Projected premium trend = 10%
 Proposed rate effective date is 10/1/2025
 Rates will be in effect for 2.5 years
Calendar Qtr EPAPR Avg EPAPR Avg On-Leveled WP
2022Q1 1,500,000 1,900 1,000
2022Q2 1,600,500 1,050 1,050
2022Q3 1,500,000 1,150 1,100
2022Q4 1,900,000 1,850 1,900
2023Q1 2,000,500 1,900 2,000
2023Q2 2,100,000 2,050 2,500
5) (1.75 points) Calculate the factor to be applied to Accident Year 2022 historical losses to trend
them to the prospective period:
 1.5% annual loss trend
 Semi-Annual policies
 Proposed rate effective date: 4/1/2025
 Rates will be in effect for 1.5 years
6) (2.75 points) Given the following information, calculate the Adjustment Factor for
3Q2023 AY Losses:
 A change was implemented on 4/1/2023 that only affects losses on policies written on or
after 4/1/2023. The direct effect of the change for semi-annual policies on an accident
year basis is estimated at +10%.
 Another change was implemented on 7/1/2023 that affects losses on policies currently
in-force at the time. The direct effect of the change for semi-annual policies on accident
year basis is estimated at -5%.
7) (2.5 points) Assuming a 15% ground-up loss trend and a $10,000 limit, calculate the impact on
the excess layer using the following claims’ total limits losses:
Claim Number Total Limits Loss (Ground-up Loss)
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CMP7000A CMP-7038B Math 263 LAW3016 CS371 STAT 334 FIN0008 ACC3004 STAT 371 ​COMP1921 MTH201 ACCT2000 UN3412 CIV6000 MATHS 3021 MATE7014 ECON1 CIBC6035 LAW121G COMM 321 CSC8204R TTM2033 CSCI 2600 MAE 115 LNG302 CENV6175W1 ECON30019 CPS2015 BST969 DDES9015 AMATH242 CS 1151 N1592 ACCT600 EG503G SMM519 EC318 Ecstatistics EEE 471 MARK2051 Topology COM00037H ACCT3000 MTHM501 EG501V COM00055H BUSN9085 GGR273 MATH 2B ITD102 MA214 ECON0060 ECE3114 ECMM447 Mechanics CCT361H5S BSAN3210 WELF2001 Fin3001 RESP5001 STA 137 Linguistics 101 CSCI368 CMPSC497 LUBS3655 OMBA 5355 BUSM2562 ​BFF5902 CYBR7001 CULT2005 ECON 7720 MTRX3760 FSE598 ​LUE1001 MGSC 7100 CS3240 COSC7500 ACCT3091 INFOGR TRAN 2080 DESIGN CIVE215001 CIVE2360 CPSC 8430 FNCE2003 Stoichiometry INFS6023 Quantitative Method Math 21D ECE5179 Design ​ECON8022 Chemical DMS 213 ADM1370 BFF5902 BFF2701 AGRI10051 AMN400 ECON7322 ​FINC5090 ​MATH1052 ​SciComp Elec4622 ​FINS5516 ENG 101 MMM143 CS431CA2 BSAN2201 EBSC7070 ES9v9-10 PLIN0009 DATA 8 MATH 101 BCPM0097 ​MAT 237 BISM2201 EEE8099 Physics 11 ECE2238B Biostat 234 ​ECON30009 INF10025 CHEM252 CCMA4008 CIVE 3007 STAT0031 ELEC ENG 3108 MGMT90140 CHEM 252 STAT3016 MMM095 ​MMGT6016 Legal STAT 311 ELEC9764 COMP 370 TCS 3053 EECS 1021 FIT1051 C/C++ EE3C COMP2003J COM398 COMP51915 Simulator FIN42330 8PRO102 PGD ELEC5160 XJCO1921 COMP5123M INFS 2042 CHE1148H ECA5313 IN3329 Microsoft Modeling B15 2TT COMP3687 COMP2432 DMS2030 KAN4TSF CFKG CSE 5322 CSE 445 STATS 3DA3 CHC5223 COMP1048 EL3105 EECS 3221 CS231 ME 4434 ITP4510 ITP4501 CSCI 5708 Controller EECE 5699 CPEN 231L CPN programs CSC8016 MATU9D2 ENGN4213 2. SVM. (10 points) Consider an SVM classifier using RBF kernel, and finish the following python code to search for the optimum kernel parameter γ. You are required to calculate the RBF function and search yourself, instead of using functions in Scikit-Learn (sklearn). def parameter search(gamma list ,Xtr,ytr,Xts,yts ,...): """ Parameters gamma list: A list of RBF kernel parameter gamma to search for Xtr: Training data, shape (ntr,nrow,ncol) ytr: Training labels, shape (ntr,) Xts: Test data, shape (nts,nrow,ncol) yts: Test labels, shape (nts,) ... Add other parameters as needed Returns: gamma optimum: The gamma with minimum error on Xts, yts """ ... return gamma optimum
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