ACTL3162 General Insurance Techniques ACTL5106 Insurance Risk Models Assignment
Due time: Friday 15th November 2019 4 pm 1 Learning outcomes
The assignment aims at developing the course learning outcomes in relation to those stated in the course outline. It also assesses the program learning outcomes “Knowledge”, “Problem solving and critical thinking”, as well as “Communication”. You are expected to demonstrate your ability to analyse an actuarial problem, apply appropriate theories and logic to interpret the problem, and develop solutions and conclusions. The communication of those will also be assessed.
2 Assignment tasks
Task 1.
You are an actuarial analyst for a general insurer who introduced a new liability insurance product to the market just over one year ago. During this time, the company has received 1,000 claims and you now believe the claims experience is significant enough for you to investigate the form of the accident severity distribution. The claims amounts are stored in LossData.xls.
Your task is to use Maximum Likelihood Estimation (MLE) to fit an appro- priate accident severity distribution for individual claims. You are required to fit the Log-normal, Gamma, Weibull and Burr XII distributions to the claims data and use appropriate goodness-of-fit tests to decide and subsequently justify which of the four distributions is the most appropriate to use for modelling the claim severity distribution. You may wish to further support your conclusions via graphical approaches.
In addition, you must briefly describe your methodology in reaching your MLE estimates of your parameters. However, providing detailed mathemat- ical formulas and code snippets is not necessary (but the entire R code or the code of other software if you are not using R must be provided in the Appendix).
1
Task 2.
An insurance company has a surplus process with a compound Poisson claims process with parameter λ. Assume that individual claim amounts X are independent and identically distributed with density of the form
p(x) = 1e−x + 2xe−x, for x > 0. 33
The insurer’s premium is paid continuously at a constant rate and is calcu- lated so that the relative security loading is 37.5%.
(a) Define the adjustment coefficient associated with this surplus process and calculate the value of this adjustment coefficient.
(b) The insurer is offered a proportional reinsurance from another company which charges a premium loading factor of 50%. If the direct insurer retains 84% of each claim, calculate (numerically) the adjustment co- efficient for the direct insurer. Find (numerically) the direct insurer’s retained proportion α ∈ [0, 1] that will maximize the adjustment coef- ficient for the direct insurer.
(c) Now consider that the insurer uses an excess of loss (EoL) reinsurance with a limit d = 3. If the premium loading factor of the EoL reinsurance is again 50%, calculate (numerically) the adjustment coefficient for the direct insurer.
(d) Now suppose the initial surplus is c0 = 1. Using the Lundberg lower and upper bounds, find a range of the probability of ruin for the direct insurer adopting the same EoL reinsurance considered in Part (c).
Additional instructions
• Answers are to be provided in Word or pdf format.
• For Task 1, your answer should include the following steps:
– Estimate the model parameters for a given model and present the fitted model
– Evaluate the quality of the given model by using graphical ap- proaches and performing hypothesis tests
(Hint: when there is no grouping in the data, the K-S and A-D tests make more sense than the χ2-test because no arbitrary deci- sions need to be made. So you do not have to perform the χ2-test in this assignment.)
2
– Determine the model that fits best using the criteria introduced in the lectures.
• Intermediate steps for questions involving any form of derivation are required. Your comments and conclusions should be well justified and charts should be used to support your conclusions where applicable.
• You are strongly recommended to use the software R for pro- gramming, although the use of other software will also be accepted. Some sample R codes for fitting are available on the course website which may be of use. In addition, feel free find packages online to perform your computations (but always check that your answer is sen- sible!).
• When making a comment or conclusion based on R outputs (or other software outputs), you should include the relevant outputs in the main body of your report. You should make sure that the marker can read and understand your arguments and statements without referring to the appendix.
• Your R codes (or codes of other software) should be included in the appendix. The marker will choose a portion of the reports to check the code. He/she will need to copy the code, run it and check whether it is correct, implementable and consistent with the output presented in your answer. Students will risk failing the assignment if the code cannot be run or the output provided in the answer is not consistent with the output generated by the code.
• There is no page limit. However, you should think of a clear and ef- fective structure for your responses. Responses provided of excessive lengths are explicitly penalised in the communications criteria.
• You should not
– Include a chunk of programming codes in the main body of your
report
– Have figures or tables that are not referred to or analysed in the main body of your report
– Include materials that are not highly relevant in the main body of your report
3
2.1 Communication skills
Students may find resources from the EDU useful – connect to the EDU website on Moodle “Write well; Learn deeply”. The student enrolment key is “ASB_LTP”.
2.2 Assignment submission procedure
Your assignment must be uploaded as a unique document (either pdf or Word document) and all parts must be in portrait format. As long as the due date is still future, you can resubmit your work; the previous version of your assignment will be replaced by the new version.
Assignments must be submitted via the Turnitin submission box that is available on the course Moodle website. Turnitin reports on any similarities between their own cohort’s assignments, and also with regard to other sources (such as the internet or all assignments submitted all around the world via Turnitin). More information is available at: [click]. Please read this page, as we will assume that you are familiar with its content.
Please note that the School of Risk and Actuarial Studies will apply the following policy on late assignments. A penalty of 25% of the mark the student would otherwise have obtained, for each full (or part) day of lateness (e.g., 0 day 1 minute = 25% penalty, 2 days 21 hours = 75% penalty). Students who are late must submit their assessment item to the LIC via e- mail. The LIC will then upload documents to the relevant submission boxes. The date and time of reception of the e-mail determines the submission time for the purposes of calculating the penalty.
You need to check your document once it is submitted (check it on-screen).
We will not mark assignments that cannot be read on screen.
Students are reminded of the risk that technical issues may delay or even pre- vent their submission (such as internet connection and/or computer break- downs). Students should then consider either submitting their assignment from the university computer rooms or allow enough time (at least 24 hours is recommended) between their submission and the due time. The Turnitin module will not let you submit a late report. No paper copy will be either accepted or graded.
In case of a technical problem, the full document must be submitted to the LIC before the due time by e-mail, with explanations about why the student was not able to submit on time. In principle, this assignment will not be marked. It is only in exceptional circumstances where the assignment was
4
submitted before the due time by e-mail that it may be marked—and this only if a valid reason is established (and the LIC has the discretion in deciding whether a given reason is valid).
2.3 Plagiarism awareness
Students are reminded that the work they submit must be their own. While we have no problem with students discussing assignment problems if they wish, the material students submit for assessment must be their own. In particular, this means that any code you present are from your own computer, which you yourself developed, without any reference to any other student’s work.
While some small elements of code are likely to be similar, big patches of identical code (even with different variable names, layout, or comments— Turnitin picks this up) will be considered as plagiarism. The best strategy to avoid any problem is not to share bits and pieces of code with other student outside your group.
Note however that you are allowed to use any R code that was made avail- able during the course (either with the lectures or developed in the tutorial exercises). You don’t need to reference them formally, and this will not be considered as plagiarism.
Students should make sure they understand what plagiarism is—cases of plagiarism have a very high probability of being discovered. For issues of collective work, having different persons marking the assignment does not decrease this probability. For more information on plagiarism, see [click].
Students should consult the “Write well; Learn deeply” website and consult
the resources provided there. In particular, all students should do the quiz
about plagiarism to make sure they know how to avoid any issue. For in-
stance, did you know that sharing any part of your work with other students
(outside your group) before the deadline is already considered as plagiarism?
1
3 Assessment criteria
Please see the file, “Rubric”.
1Yes, that’s right, just sending it, even if the third party promises not to copy, is already plagiarism in the UNSW policy!
5
Reviews
There are no reviews yet.