Introduction

This course is tailored for the validation of Short Term Actuarial Mathematics (STAM) exam by Society of Actuaries (SOA). The main materials include (i) probability models commonly used for severity, frequency, risk aggregations, coverage modifications, and (ii) risk indications commonly used in credibility theory and reinsurance. The aim is to build up probability and statistical foundation for graduate students with concentration in actuarial science, and the focus is put on calculations concerned with coverage modifications and risk measures, constructing and estimation of parametric models. Also, the attention is paid to the basics of insurance and reinsurance, the calculation of premiums and reserve for the short-term insurance as well.

Prerequisites: MA540, MA541
Cross-listing: None

Course Objective

The students will learn and understand the following actuarial models and the concerned associated probability and statistical methods:
• Commonly used severity and frequency models
• Modification of insurance coverage
• Most popular risk measures
• Parametric statistical models
• Credibility models and criteria
• Insurance and reinsurance coverages for short-term insurances
• Premium and reserve for short-term insurance coverages

Course Outcomes

• Compare two distributions based on tail characteristics, including moments, ratios of moments, limiting tail behavior, hazard rate function, and mean excess function.
• Derive and perform calculations with the zero-truncated and zero-modified versions of frequency distributions.
• Calculate aggregate loss distribution in case of various severity distributions.
• Evaluate the coverage modifications, including deductibles, coverage limits, and coinsurance.
• Calculate Value-at-Risk and Tail-Value-at-Risk, and explain the desirable properties of a risk measure and determine whether a risk measure has these properties.
• Use the delta method to estimate the variance of the maximum likelihood estimator of a function of the parameter(s), and utilize Bayesian method to estimate the parameters for severity, frequency, and aggregate distributions.
• Utilize Buhlmann and Buhlmann-Straub models and understand their relationship to Bayesian models, and apply empirical Bayesian method in nonparametric and semiparametric cases.
• Describe the types of policy limits and coverage modifications, the operation of basic forms of proportional and excess of loss reinsurance, and derive the distribution of claim amounts paid by the insurer and reinsurer under various forms of reinsurance.
• Describe the underlying statistical models and apply techniques for estimating unpaid losses from a run-off triangle, using chain ladder, average cost per claim and Bornhuetter Ferguson.

Textbook

• Required textbook Loss Models: From Data to Decisions， Fourth Edition, 2012
  
• Recommended texts
  Introduction to Ratemaking and Loss Reserving for Property and Casualty Insurance Fourth Edition, 2015, Brown and Lennox, ACTEX, ISBN: 978-1625424747.
  
• Syllabus and study materials, SOA
  Exam STAM: Short-Term Actuarial Mathematics
  

Grading Policies

		Weights
1	Homework	50%
2	Mid-term	20%
3	Final	30%
	Maximum Possible	100%