Syllabus - ACMA 490-3/STAT 890-4
Selected Topics in Actuarial Science: Risk Measures and Ordering
Department of Statistics and Actuarial Science, Faculty of Science, Simon Fraser University
Spring 2006
Instructor: Cary Tsai (cltsai@sfu.ca)
K 10548 Tel: 604-268-7044
Formula: 3-0-0/4-0-0
Prerequisite: ACMA 335 / STAT 450
Lecture Hours/Rooms: T : 08:30-10:20 @ AQ 5018
R : 08:30-10:20 @ RCB 8100 (8:30-9:20 is for STAT 890 only)
Office Hours: T: 11:30-12:20 and 15:30-16:20
R: 11:30-12:20 and 16:30-17:20
Outline:
This course studies the actuarial risks. A variety of risk measures and orders, and premium calculation
principles and associated properties will be introduced. They include the following:
~ Stochastic order
~ Stop-loss order
~ Higher degree order
~ Premium calculation principles
~ Properties of premium calculation principles
~ Ordering of risks under proportional hazards transforms
~ Comonotonicity
~ Actuarial applications
Textbook: Lecture notes and selected papers.
Selected papers:
(1). Shaun S. Wang (1995),
“Insurance pricing and increased limits ratemaking by proportional hazards transforms”,
Insurance: Mathematics and Economics, 17, 43-54.
(2). Shaun S. Wang (1996),
“Ordering of risks under PH-transforms”, Insurance: Mathematics and Economics, 18, 109-114.
(3). Shaun S. Wang (1996),
“Premium calculation by transforming the layer premium density”, ASTIN Bulletin, 26, 71-92.
(4). Shaun S. Wang, Virginia R. Young and Harry H. Panjer (1997),
“Axiomatic characterization of insurance prices”, Insurance: Mathematics and Economics, 21, 173-183.
(5). Shaun S. Wang and Jan Dhaene (1998),
“Comonotonicity, correlation order and premium principles”,
Insurance: Mathematics and Economics, 22, 235-242.
(6). Shaun S. Wang and Virginia R. Young (1998),
“Ordering risks: Expected utility theory versus Yaari's dual theory of risk”,
Insurance: Mathematics and Economics, 22, 145-161.
(7). Shaun S. Wang (1998),
“An actuarial index of right-tail risk”, North America Actuarial Journal, 2 (2), 88-101.
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Evaluation:
Regular assignments and project(s) throughout the semester.
Midterm: 8:30-10:20AM, February 23, Thursday, 2006 (may be altered depending on teaching progress).
Final exam: 8:30-11:30AM, April 13, Thursday, 2006 (Check the classroom and final exam schedule).
Assignments (once available) and selected references can be downloaded from
www.stat.sfu.ca/~cltsai/ACMA490/ACMA490_0601.htm.
Missing an exam will result in a mark of 0 unless the student was prevented from taking it due to
medical reasons with convincing evidence. A student present at the start of an exam will have his/her
exam marked even if he/she leaves early for any reason. Should you miss an exam, you must let the
instructor know as soon as possible. Under no circumstances will make up exams be given.
Under no circumstances will late assignments and project(s) be accepted.
The final grade (A+, A, ..., F) will be allocated according to the student's achievement in the course.
Grading Scheme: The grading is subject to change.
Assignments
Project
Midterm
Final Exam
Reading and Presentations
ACMA 490
10%
20%
30%
40%
0%
STAT 890
10%
20%
30%
30%
10%
Lectures Rescheduled:
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
1/10
1/17
1/24
1/31
2/07
2/14
2/21
2/28
3/07
3/14
3/21
3/28
4/04
4/11
Tuesdays, 8:30-10:20AM @ AQ5018
ACMA 490
STAT 890
ACMA 490
STAT 890
ACMA 490
STAT 890
Reading Break
ACMA 490
STAT 890
ACMA 490
STAT 890
ACMA 490
STAT 890
No lectures
1/12
1/19
1/26
2/02
2/09
2/16
2/23
3/02
3/09
3/16
3/23
3/20
4/06
4/13
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Thursdays, 8:30-10:20AM @ RCB 8100
ACMA 490
ACMA 490
ACMA 490
ACMA 490
ACMA 490
ACMA 490
Midterm
ACMA 490
ACMA 490
ACMA 490
ACMA 490
ACMA 490
ACMA 490
Final Exam, 8:30-11 :30AM
Insurance Premiums, M. J. Goovaerts, F. De Vylder, and J. Haezendonck, 1984, North-Holland, Amsterdam.
Effective Actuarial Methods, M. J. Goovaerts, . Kaas, A.E. Van Heerwaarden, and T. Bauwelinckx, 1990,
North-Holland, Amsterdam.
Ordering of Risks: Theory and Actuarial Applications, A. Van Heerwaarden, 1991, Thesis/Tinbergen
Institute, Amsterdam.
Ordering of Actuarial Risks, R. Kaas, A.E. Van Heerwaarden, and M.J. Goovaerts, 1994, Caire Education
Series 1, Brussels, Belgium.
Stochastic Orders and their Applications, M. Shaked and J.G. Shanthikumar, 1994, Academic Press, San
Diego.
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