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, SimonFraserUniversity

Instructor: / Cary Tsai () / Spring 2006
K 10548 Tel: 604-268-7044 / Formula: 3-0-0/4-0-0
Lecture Hours/Rooms: / T: 08:30-10:20 @ AQ 5018 / Prerequisite: ACMA335/STAT450
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.

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

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.

GradingScheme: The grading is subject to change.

ACMA 490 / STAT 890
Assignments / 10% / 10%
Project / 20% / 20%
Midterm / 30% / 30%
Final Exam / 40% / 30%
Reading and Presentations / 0% / 10%

LecturesRescheduled:

Week

/

Tuesdays,8:30-10:20AM @ AQ5018

/

Thursdays, 8:30-10:20AM @ RCB 8100

1

/

1/10

/

ACMA 490

/

1/12

/ ACMA 490

2

/

1/17

/

STAT 890

/

1/19

/ ACMA 490

3

/

1/24

/

ACMA 490

/

1/26

/ ACMA 490

4

/

1/31

/

STAT 890

/

2/02

/ ACMA 490

5

/

2/07

/

ACMA 490

/

2/09

/ ACMA 490

6

/

2/14

/

STAT 890

/

2/16

/ ACMA 490

7

/

2/21

/

Reading Break

/

2/23

/ Midterm

8

/

2/28

/

ACMA 490

/

3/02

/ ACMA 490

9

/

3/07

/

STAT 890

/

3/09

/ ACMA 490

10

/

3/14

/

ACMA 490

/

3/16

/ ACMA 490

11

/

3/21

/

STAT 890

/

3/23

/ ACMA 490

12

/

3/28

/

ACMA 490

/

3/20

/ ACMA 490

13

/

4/04

/

STAT 890

/

4/06

/

ACMA 490

14

/

4/11

/

No lectures

/

4/13

/

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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