Math 404 HW 1 - Spring 2024 - Actuarial Loss Elimination Ratio and Distribution Estimation

Sep 27, 2026

Actuarial Mathematics homework for Math 404 (HW 1) for Spring 2024, due Thursday Jan. 25, consisting of six problems. The questions focus on estimating loss elimination ratio LER under Pareto models with deductibles, computing distribution functions and hazard-related quantities for Pareto, and evaluating expected values under exponential and lognormal assumptions. Additional tasks estimate Poisson probabilities for small counts and compute E(X ∧ 500) for a lognormal variable using provided parameter estimates. The document emphasizes graded process work, solving without copying, and submitting solutions on separate sheets.

LanguageEnglish

CategoryExam

FormatPDF

Pages1

Reading Time3 min

AccessFree to download

Homework Instructions

Submission and Academic Integrity

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Math 404 HW 1 Spring 2024 . Due Thursday, Jan. 25. 1 page 6 questions. course webpage: [http://parker.ad.siu.edu/Olive/M404.html](http://parker.ad.siu.edu/Olive/M404.html) Place your solutions on a separate sheet of paper. DO NOT place solutions side by side. You may use both the front and the back of each sheet. Google “soa exam c sample questions” to Exam C Sample Questions (200 pages) and Solutions (107 pages) . Sometimes HW problems will come from these questions. These pages are modi􀀌ed sometimes. [From www.soa.org:](From www.soa.org:) click on Education & Exams, then then Associate of the Society of Actuaries (ASA), then scroll down and click on Advanced Short-Term Actuarial Mathematics (ASTAM) Exam, then the Advanced Short-Term Actuarial Mathematics (ASTAM) Exam Study page. This webpage will also have questions and solutions. For Math 403 type questions, click on Fundamentals of Actuarial Mathematics (FAM) Exam, then the FAM Exam Study page where the FAM-S problems are for Math 403 . YOU ARE BEING GRADED FOR WORK NOT JUST THE FINAL ANSWER. Asa rule of thumb, you should have some idea of what you were doing, even without the book or notes. You are encouraged to form groups to discuss ideas and HW problems, but do not copy. Assume X 􀀕 0 unless told otherwise. 1) Suppose X 􀀘 single parameter Pareto(􀀋,􀀒) . If ˆ􀀋 = 2 and ˆ􀀒 = 100, estimate the loss elimination ratio LER(200) if there is a deductible of 200. 2) Suppose X 􀀘 two parameter Pareto(􀀋,􀀒) . If ˆ􀀋 = 2 and ˆ􀀒 = 100, estimate the loss elimination ratio LER(200) if there is a deductible of 200 . 3) Suppose X 􀀘 Pareto(􀀋,􀀒) . If ˆ􀀋 = 1 and ˆ􀀒 = 1000, for x > 0 , estimate a) F(x) b) h(x) . Hint: Use ˆf(x) = d~~ ~~ ˆdx F(x) . 4) Suppose X 􀀘 EXP (􀀒) with ˆ􀀒 = 1000 . If the deductible d = 500, estimate a) E (YP ) b) E (YL ) . 5) Suppose N1 , ... , Nn are iid Poisson(􀀕) with N = ˆ􀀕 = 5 . Estimate a) P (N = 0) and b) P (N = 1) . (Use at least four digits after leading zeros, eg 0.03401.) 6) Suppose X 􀀘 LN (􀀖,􀀛) with ˆ􀀖 = 5 .3949 and ˆ􀀛2 = 1 .1218. Estimate E (X ∧ 500) . Hint: See Exam C Question 6 from the second paragraph of this handout. Note that ˆ􀀛 = √ˆ􀀛2 .

FAQs

When is Math 404 HW 1 due and what is the expected submission format?

It is due Thursday, Jan. 25. Solutions must be placed on a separate sheet of paper, not side by side; both front and back can be used.

How are the loss elimination ratio problems set up?

The homework asks for LER(200) under one-parameter and two-parameter Pareto assumptions using specified estimated parameters and a deductible of 200.

What distribution estimation tasks appear in the later problems?

The later problems request estimating F(x) and h(x) for a Pareto model, expected values under an exponential model with a deductible, Poisson probabilities for N=0 and N=1, and E(X ∧ 500) for a lognormal model.

Sep 27, 2026

Uploaded by Olivia Brown