1. Instructor:
Dr. Tao Pang
Office:
Harrelson Hall 226
Telephone:
513-2110
Email:
tpang@math.ncsu.edu
Office hours:
T, Th 1:30pm-2:30pm or by appointment.
2. Prerequisites:
Knowledge of long-term models as developed in MA 422—Long-Term Actuarial
Models is not assumed, but the student should be familiar with basic probability
concepts and distributions.
3. Textbook:
Actuarial Mathematics by Bowers, Gerber, Hickman, Jones
and Nesbitt, 2nd Ed. /1997, required.
There are also some optional textbooks. Please see reading schedule.
4. Course Objectives:
This course introduces students to risk management systems by developing
some short-term probability models for potential losses. Short-term probability
models are appropriate for most traditional property, liability, health
and group insurance systems. With the proliferation of new instruments
and new strategies for risk management, insurance systems have found applicability
in many areas that have never been considered insurance in the past, such
as conventional business decisions where unfavorable outcomes could threaten
the viability of the enterprise.
5. Outline of Course:
Characterizing Frequency
Distributions and Loss Distributions (8 classes): Characterizing
distributions in terms of their parameters and moments; techniques for
creating new families of distributions; applications for which these distributions
are used and the reasons why they are used.
Individual Risk Models
(5 classes): Probability distribution of an aggregate loss
modeled as the sum of the losses from a fixed number of components of a
portfolio of risks; tabulating a distribution by exact and approximate
methods; applications.
Collective Risk Models
(5 classes): Probability distribution of an aggregate loss modeled
as the sum of a random number of individual losses; compound distributions
and their properties; tabulating a distribution by exact and approximate
methods; applications.
Stochastic Surplus
Processes (5 classes): Discrete-time and continuous-time Poisson
surplus processes; analyzing the probability of ruin; characteristics of
the distribution of the amount of surplus.
Applications of Risk
Models (4 classes): A collective model for disability insurance;
approximating the individual risk model by a compound Poisson model; an
analysis of reinsurance using ruin theory
6. Reading Schedule:
There are no reading assignments during the study of the characteristics
of frequency distributions and loss distributions. The basis of this material
can be found in textbooks such as Probability for Risk Management
by
Hassett and Stewart and Loss Models by Klugman, Panjer and
Willmot. Students are referred to these and other textbooks
such as Econometric Models and Economic Forecasts (4th Ed.)
by Robert Pindyck and Daniel Rubinfeld for additional insights and exercises.
The development of the individual and collective risk theory follows the approach taken in the Actuarial Mathematics textbook. The topics that we cover correlate to the chapters in Actuarial Mathematics as follows:
Individual Risk Models:
Chapter 2
Collective Risk Models:
Chapter 12
Stochastic Surplus
Processes:
Chapter 13
Applications of Risk
Theory:
Chapter 14
Students use the textbook for solving homework problems and developing a deeper understanding of the material presented in class, but there is no formal reading schedule.
7. Grade Policy
9. Academic Integrity
Plagiarism and cheating are attacks on the very foundation of academic
life, and cannot be tolerated within universities. Section eight (8) of
the Code defines academic dishonesty and provides information on potential
sanctions for violators of academic integrity. The NCSU Academic Integrity
statement can be found at http://www.ncsu.edu/provost/academic_policies/integrity/reg.htm
10. Disability Services for Students
Students with a disability must contact the NCSU Disability Services.
Additional information: http://www.ncsu.edu/equal_op/dss/.