
Numerical Analysis
10th Edition
ISBN: 9781305253667
Author: Richard L. Burden, J. Douglas Faires, Annette M. Burden
Publisher: Cengage Learning
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Chapter 1.2, Problem 3ES
a.
To determine
The largest interval in which
b.
To determine
The largest interval in which
c.
To determine
The largest interval in which
d.
To determine
The largest interval in which
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PEER REPLY 1:
Choose a classmate's Main Post and review their decision making process.
1. Choose a risk level for each of the states of nature (assign a probability
value to each).
2. Explain why each risk level is chosen.
3. Which alternative do you believe would be the best based on the maximum
EMV?
4. Do you feel determining the expected value with perfect information
(EVWPI) is worthwhile in this situation? Why or why not?
Questions
An insurance company's cumulative incurred claims for the last 5 accident years are given
in the following table:
Development Year
Accident Year 0
2018
1 2 3 4
245 267 274 289 292
2019
255 276 288 294
2020
265 283 292
2021
263 278
2022
271
It can be assumed that claims are fully run off after 4 years. The premiums received for
each year are:
Accident Year Premium
2018
306
2019
312
2020
318
2021
326
2022
330
You do not need to make any allowance for inflation.
1. (a) Calculate the reserve at the end of 2022 using the basic chain ladder method.
(b) Calculate the reserve at the end of 2022 using the Bornhuetter-Ferguson method.
2. Comment on the differences in the reserves produced by the methods in Part 1.
Chapter 1 Solutions
Numerical Analysis
Ch. 1.1 - Show that the following equations have at least...Ch. 1.1 - Show that the following equations have at least...Ch. 1.1 - Find intervals containing solutions to the...Ch. 1.1 - Find intervals containing solutions to the...Ch. 1.1 - Find maxaxb |f(x)| for the following functions and...Ch. 1.1 - Find maxaxb | f(x)| for the following functions...Ch. 1.1 - Show that f(x) is 0 at least once in the given...Ch. 1.1 - Suppose f C[a, b] and f (x) exists on (a, b)....Ch. 1.1 - Let f(x) = x3. a. Find the second Taylor...Ch. 1.1 - Find the third Taylor polynomial P3(x) for the...
Ch. 1.1 - Find the second Taylor polynomial P2(x) for the...Ch. 1.1 - Repeat Exercise 11 using x0 = /6. 11. Find the...Ch. 1.1 - Prob. 13ESCh. 1.1 - Prob. 14ESCh. 1.1 - Prob. 15ESCh. 1.1 - Use the error term of a Taylor polynomial to...Ch. 1.1 - Use a Taylor polynomial about /4 to approximate...Ch. 1.1 - Let f(x) = (1 x)1 and x0 = 0. Find the nth Taylor...Ch. 1.1 - Let f(x) = ex and x0 = 0. Find the nth Taylor...Ch. 1.1 - Prob. 20ESCh. 1.1 - The polynomial P2(x)=112x2 is to be used to...Ch. 1.1 - Use the Intermediate Value Theorem 1.11 and Rolles...Ch. 1.1 - Prob. 23ESCh. 1.1 - In your own words, describe the Lipschitz...Ch. 1.2 - Compute the absolute error and relative error in...Ch. 1.2 - Compute the absolute error and relative error in...Ch. 1.2 - Prob. 3ESCh. 1.2 - Find the largest interval in which p must lie to...Ch. 1.2 - Perform the following computations (i) exactly,...Ch. 1.2 - Use three-digit rounding arithmetic to perform the...Ch. 1.2 - Use three-digit rounding arithmetic to perform the...Ch. 1.2 - Repeat Exercise 7 using four-digit rounding...Ch. 1.2 - Repeat Exercise 7 using three-digit chopping...Ch. 1.2 - Prob. 10ESCh. 1.2 - Prob. 11ESCh. 1.2 - Prob. 12ESCh. 1.2 - Let f(x)=xcosxsinxxsinx. a. Find limx0 f(x). b....Ch. 1.2 - Let f(x)=exexx. a. Find limx0(ex ex )/x. b. Use...Ch. 1.2 - Use four-digit rounding arithmetic and the...Ch. 1.2 - Prob. 16ESCh. 1.2 - Prob. 17ESCh. 1.2 - Repeat Exercise 16 using four-digit chopping...Ch. 1.2 - Use the 64-bit-long real format to find the...Ch. 1.2 - Prob. 23ESCh. 1.2 - Discuss the difference between the arithmetic...Ch. 1.2 - Prob. 2DQCh. 1.2 - Discuss the various different ways to round...Ch. 1.2 - Discuss the difference between a number written in...Ch. 1.3 - The Maclaurin series for the arctangent function...Ch. 1.3 - Prob. 4ESCh. 1.3 - Prob. 5ESCh. 1.3 - Find the rates of convergence of the following...Ch. 1.3 - Find the rates of convergence of the following...Ch. 1.3 - Prob. 8ESCh. 1.3 - Prob. 9ESCh. 1.3 - Suppose that as x approaches zero,...Ch. 1.3 - Prob. 11ESCh. 1.3 - Prob. 12ESCh. 1.3 - Prob. 13ESCh. 1.3 - Prob. 14ESCh. 1.3 - a. How many multiplications and additions are...Ch. 1.3 - Write an algorithm to sum the finite series i=1nxi...Ch. 1.3 - Construct an algorithm that has as input an...Ch. 1.3 - Let P(x) = anxn + an1xn1 + + a1x + a0 be a...Ch. 1.3 - Prob. 4DQCh. 1.3 - Prob. 5DQCh. 1.3 - Prob. 6DQ
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