SDST4901 Risk Theory II (6 credits) Academic Year 2025
Offering Department SCDS (Department of Statistics and Actuarial Science) Quota ---
Course Co-ordinator TBC, SCDS (Department of Statistics and Actuarial Science) < ugenq@hku.hk >
Teachers Involved
Course Objectives This course is an advanced course in risk theory which extends various topics discussed in SDST3906. It discusses utility theory, ruin theory, aggregate claims process, and related topics.
Course Contents & Topics Utility theory; discrete ruin model; compound Poisson risk model; ruin probability; reinsurance; adjustment coefficient; Lundbergs inequality; Tijms approximation; non-homogeneous birth process; contagion model; mixed Poisson process; inflation model; IBNR (Incurred But Not Reported) claims; mixed Erlang distributions; stop-loss moments; equilibrium distributions.
Course Learning Outcomes
On successful completion of this course, students should be able to:

CLO 1 understand utility theory including some commonly used utility functions, Jensens inequality, risk aversion and utility maximization
CLO 2 define discrete and continuous ruin models
CLO 3 calculate the adjustment coefficient, Lundbergs inequality and Tijms approximation in ruin theory
CLO 4 understand the effect of reinsurance and change of parameters on ruin probability
CLO 5 understand non-homogeneous birth process and its applications as contagion models for claim frequencies
CLO 6 understand mixed Poisson process and its applications including the inflation model and the IBNR model
CLO 7 derive the relationship between stop-loss moments and equilibrium distributions
Pre-requisites
(and Co-requisites and
Impermissible combinations)		 Pass in SDST3906
Only for students admitted in 2025 and thereafter.
Course Status with Related Major/Minor /Professional Core 2U000C00 Course not offered under any Major/Minor/Professional core
2025 BSc in Actuarial Science ( Disciplinary Elective )
Course to PLO Mapping 2025 BSc in Actuarial Science < PLO 1,3,5 >
Offer in 2025 - 2026 N        Examination
Offer in 2026 - 2027 N
Course Grade A+ to F
Grade Descriptors
A Demonstrate thorough mastery at an advanced level of extensive knowledge and skills required for attaining all the course learning outcomes. Show strong analytical and critical abilities and logical thinking, with evidence of original thought, and ability to apply knowledge to a wide range of complex, familiar and unfamiliar situations. Apply highly effective organizational and presentational skills.
B Demonstrate substantial command of a broad range of knowledge and skills required for attaining at least most of the course learning outcomes. Show evidence of analytical and critical abilities and logical thinking, and ability to apply knowledge to familiar and some unfamiliar situations. Apply effective organizational and presentational skills.
C Demonstrate general but incomplete command of knowledge and skills required for attaining most of the course learning outcomes. Show evidence of some analytical and critical abilities and logical thinking, and ability to apply knowledge to most familiar situations. Apply moderately effective organizational and presentational skills.
D Demonstrate partial but limited command of knowledge and skills required for attaining some of the course learning outcomes. Show evidence of some coherent and logical thinking, but with limited analytical and critical abilities. Show limited ability to apply knowledge to solve problems. Apply limited or barely effective organizational and presentational skills.
Fail Demonstrate little or no evidence of command of knowledge and skills required for attaining the course learning outcomes. Lack of analytical and critical abilities, logical and coherent thinking. Show very little or no ability to apply knowledge to solve problems. Organization and presentational skills are minimally effective or ineffective.
Communication-intensive Course N
Course Type Lecture-based course
Course Teaching
& Learning Activities
Activities Details No. of Hours
Lectures 36.0
Tutorials 12.0
Reading / Self study 100.0
Assessment Methods
and Weighting
Methods Details Weighting in final
course grade (%)		 Assessment Methods
to CLO Mapping
Assignments Coursework (assignments, tutorials, and a class test) 25.0 1,2,3,4,5,6
Examination One 3-hour written examination 75.0 1,2,3,4,5,6
Required/recommended reading
and online materials		 Klugman S.A., Panjer H.H., & Willmot G.E.: Loss Models: From Data to Decisions (John Wiley & Sons, 2007, 3rd edition).
Kaas R., Goovaerts M., Dhaene J., & Denuit M.: Modern Actuarial Risk Theory (Springer, 2004, 1st edition).
Bowers N.L., Gerber H.U., Hickman J.C. & Jones D.A.: Actuarial Mathematics (Society of Actuaries, 1997, 2nd edition).
Willmot G.E. & Lin X.S.: Lundberg Approximations for Compound Distributions with Insurance Applications (Springer, 2000, 1st edition).
Course Website http://moodle.hku.hk
Additional Course Information NIL