UNIVERSITY OF CONNECTICUT

Math 395

# Spring 2004

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

# Context for the Course

Partial Preparation for SOA/CAS Exam 3 (Actuarial Models)

(Thursday May 13)

# Specific Course Content

Claim Risk Models and Ruin Models

(Sections D, E, F, and G of the attached Exam 3 Outline of Topics)

# Required Texts

Klugman, et al.: Loss Models: From Data To Decisions

Klugman: Society of Actuaries Study Note 3-23-02 (replaces chapter 2 of Loss Models)

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

# For Future InDepth Study

(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