UNIVERSITY OF CONNECTICUT
Math 395
Classes: 3:00 4:15 MW Instructor: James Bridgeman, FSA
MSB 311 MSB 408 phone (860) 486-8382
Office hours: 12:00 1:30 M bridgeman@math.uconn.edu
2:30 3:30 Th http://www.math.uconn.edu/~bridgeman
1:30 3:00 F course web site : www.math.uconn.edu/~bridgeman/math395/index.html
Or by appointment
Partial Preparation for SOA/CAS Exam 3 (Actuarial Models)
(Thursday May 13)
Claim Risk Models and Ruin Models
(Sections D, E, F, and G of the attached Exam 3 Outline of Topics)
Klugman, et al.: Loss Models: From Data To Decisions
Klugman: Society of Actuaries Study Note 3-23-02 (replaces chapter 2 of Loss Models)
(download from www.soa.org)
Bowers, et al.: Actuarial Mathematics (Second Edition)
Batten & London: A Guide for the Actuarial Student
Gauger: ACTEX Study Manual for Exam 3 (Vols. I and II)
Jones: Actuarial Models and Modeling: An Interactive Approach
Panjer & Willmot:
Insurance Risk Models
Ross: Introduction to Probability Models (Seventh Edition)
Ross: Simulation (Third Edition)
Society of Actuaries: Study Note Package for Exam 3
(well beyond exam or
course requirements)
Daykin, et al.: Practical Risk Theory for Actuaries
de Vylder: Advanced
Risk Theory -- a self-contained introduction
Maerchaert&Scheffler, Limit Distributions for Sums of Independent Random Vectors heavy tails in theory and practice
4 Review Assignments 40%
` Final Exam 35%
Paper and Project(s) 25%
Exam 3 Outline of Topics
A. Survival
Models [Math 287/387]
1. Stochastic and Deterministic Survival Models (Bowers, Ch. 3)
B. Contingent Payment Models [Math 287/387 and 288/388]
1. Life Insurance (Bowers, Ch. 4)
2. Life Annuities (Sec. 5.1 5.4)
3. Benefit Premiums (Sec. 6.1 6.4)
4. Benefit Reserves (Sec. 7.1 7.6)
5 . Reserve Analysis (Sec. 8.1 8.4)
6. Multiple Life Functions (Sec. 9.1 9.8 (excl. 9.6.2))
7. Multiple Decrement Models (Ch. 10 (excl. 10.5.2 & 10.5.5),
Sec. 11.1 11.3))
C. Stochastic Process Models [Math 232 or Stat 235]
1. Introduction (Ross, Introduction to Probability Models, Sec. 2.8)
2. Discrete-Time Markov Chains (Sec. 4.1 4.4, 4.5.1, 4.6)
3. Poisson Processes (Sec. 5.3 5.4)
4. Brownian Motion (Sec. 10.1 10.3)
D. Claim Severity (& Related) Models [Math 395]
1. Introduction (Klugman, Loss Models, Sec. 1.3)
2. Probability Framework (Klugman, study note, Ch. 1 3)
3. Continuous Parametric Distributions (Ch. 4)
4. Coverage Modifications & Examples (Ch. 5 6)
E. Claim Frequency Models [Math 395]
1. Introduction (Klugman, Loss Models, Sec. 1.3 and 3.1)
2. Poisson Distribution (Sec. 3.2.1 3.2.2)
3. Negative Binomial Distribution (Sec. 3.3.1 3.3.2)
4. Binomial Distribution (Sec. 3.4.1)
5. (a,b,0) Class of Distributions (Sec. 3.5.1 (thru 1st full paragraph p. 222))
6. Compound Frequency Distributions (pp. 236 240 (excl. Ex. 3.15 & Th. 3.4))
7. Exposure Considerations (pp. 263 264)
8. Severity Modifications (pp.266 267)
F. Aggregate Claim Distribution Models [Math 395]
1. Introduction (Klugman, Sec. 1.4 and 4.1)
2. Model Choices (Sec. 4.2)
3. Compound Model (Sec. 4.3 4.4*)
4. Computing the Aggregate Distribution (Sec. 4.5)
5. Recursive Methods (Sec, 4.6 (excl. 4.6.2 4.6.5))
6. Simulation Methods (Sec. 4.8)
G. Ruin Models
[Math 395]
1. Introduction (Klugman, Sec. 6.1 6.2; Bowers, Sec. 13.1)
2. Discrete-Time Models
a. Finite Ruin Horizon (Klugmanm Sec, 6.3 (excl. 6.3.2.2))
b. Infinite Ruin Horizon (Bowers, Sec. 13.2 (excl. autoregressive model))
3. Continuous-Time Models
a. Properties (Bowers, Sec. 13.3)
b. Ruin Probabilities (Sec. 13.4)
c. Distribution of First Surplus Strain (Sec. 13.5)
d. Distribution of Maximum Aggregate Loss (Sec. 13.6)
H. Model Simulation [Math 286/366]
1. Introduction (Ross, Simulation, Ch. 1)
2. Pseudorandom Number Generation (Sec. 3.1)
3. Generating Discrete Random Variable (Sec. 4.1 4.3)
4. Generating Continuous Random Variables (Sec. 5.1, 5.2, 5.4)
* Klugman, Sec. 4.4 is not part of the Exam 3 Syllabus but provides useful illustrations of the compound model that have application in ruin theory, and is included in Math 395.
Intended
Pace for Math 395
Week of
|
Portion of Outline to be Covered |
|
|
Jan. 21 |
D.1 D.2 |
Jan. 28 |
D.2 D.3 plus generating functions & Faa |
Feb. 4 |
D.3 D.4 plus surface interpretation |
Feb. 11 |
D.4 - E.1 |
Feb. 18 |
E.2 E.3 Review Assignment on D (Severity Models, etc) |
Feb. 25 |
E.4 E.6 |
Mar. 3 |
E.6 E.8 |
Mar. 17 |
F.1 F.3 Review Assignment on E (Frequency Models) |
Mar. 24 |
F.3 F.5 |
Mar. 31 |
F.6 G.1 |
Apr. 7 |
G.2 Review Assignment on F (Aggregate Models) |
Apr. 14 |
G.3.a G.3.b |
Apr. 21 |
G.3.c G.3.d |
Apr. 28 |
Project Reviews Review Assignment on G (Ruin Models) |
|
Final Exam TBD week of May 3 - 8 |