SYLLABUS of BASIC EDUCATION 2021 Modern Actuarial Statistics-I – Exam MAS-I

SYLLABUS OF BASIC EDUCATION 2021 Modern Actuarial Statistics-I – Exam MAS-I The syllabus for this four-hour exam is defined in the form of learning objectives, knowledge statements, and readings. LEARNING OBJECTIVES set forth, usually in broad terms, what the candidate should be able to do in actual practice. Included in these learning objectives are certain methodologies that may not be possible to perform on an examination, such as calculating the Hat Matrix for a complex Generalized Linear Model, but that the candidate would still be expected to explain conceptually in the context of an examination. KNOWLEDGE STATEMENTS identify some of the key terms, concepts, and methods that are associated with each learning objective. These knowledge statements are not intended to represent an exhaustive list of topics that may be tested, but they are illustrative of the scope of each learning objective. READINGS support the learning objectives. It is intended that the readings, in conjunction with the material on earlier examinations, provide sufficient resources to allow the candidate to perform the learning objectives. Some readings are cited for more than one learning objective. The CAS Syllabus & Examination Committee emphasizes that candidates are expected to use the readings cited in this Syllabus as their primary study materials. Thus, the learning objectives, knowledge statements, and readings complement each other. The learning objectives define the behaviors, the knowledge statements illustrate more fully the intended scope of the learning objectives, and the readings provide the source material to achieve the learning objectives. Learning objectives should not be seen as independent units, but as building blocks for the understanding and integration of important competencies that the candidate will be able to demonstrate. Note that the range of weights shown should be viewed as a guideline only. There is no intent that they be strictly adhered to on any given examination—the actual weight may fall outside the published range on any particular examination. The overall section weights should be viewed as having more significance than the weights for the individual learning objectives. Over a number of years of examinations, absent changes, it is likely that the average of the weights for each individual overall section will be in the vicinity of the guideline weight. For the weights of individual learning objectives, such convergence is less likely. On a given examination, in which it is very possible that not every individual learning objective will be tested, there will be more divergence of guideline weights and actual weights. Questions on a given learning objective may be drawn from any of the listed readings, or a combination of the readings. There may be no questions from one or more readings on a particular exam. After each set of learning objectives, the readings are listed in abbreviated form. Complete text references are provided at the end of this exam syllabus. Items marked with a bold OP (Online Publication) are available at no charge and may be downloaded from the CAS website. Please check the “Syllabus Updates” section of the CAS Web Site for any changes to the Syllabus. A thorough knowledge of calculus and probability is assumed, as is familiarity with discounting cash flows. Materials for Study, 2021 Exam MAS-I Exam MAS-I-1 © 2020, 2021, Casualty Actuarial Society, All Rights Reserved Casualty Actuarial Society, 4350 North Fairfax Drive, Suite 250, Arlington, VA 22203 casact.org SYLLABUS OF BASIC EDUCATION 2021 Modern Actuarial Statistics-I – Exam MAS-I Given the material covered on Section C, we assume that the candidate has knowledge of Linear Algebra concepts at the level commonly assumed as a prerequisite to taking an undergraduate level course in regression analysis. The insurance terminology used in questions for Exam MAS-I will not assume prior knowledge of either reserving or ratemaking actuarial practice, but we may include problems with insurance terms consistent with those stated in the Knowledge Statements for section B.3. The Probability Models section (Section A) covers Stochastic Processes, Markov Chains and Survival Models along with a simplified version of Life Contingencies. Survival models are covered in depth as part of probability modeling in generic terms. Markov Chains provide the means to model how an entity can move through different states. Life Contingencies problems can be viewed as discounted cash flow problems that include the effect of probability of payment and are covered through a Study Note linking the generic survival model concepts to a subset of life actuarial concepts to illustrate how to calculate annuities or single premium insurance amounts. In general, the material covered under the Statistics section (Section B) covers topics that would be commonly found in a second semester course of a two semester Probability & Statistics sequence at the undergraduate level. Coverage of the topics listed under the Statistics section will vary by college and the candidate may need to supplement that course work with additional reading and problem-solving work from the suggested textbooks listed at the end of Section B. Extended Linear Models including Generalized Linear Models, a predictive modeling technique commonly used to construct classification plans, are covered in Section C. The ordinary least squares model is covered as one member of the exponential family under the Extended Linear Models section. Many textbooks covering this topic, including the textbook on the syllabus, use statistical software to illustrate the concepts covered in examples, since using a calculator to solve a realistic problem is impractical. While we are not testing a candidate’s ability to write R code, some of the examples in the textbooks cited in the Readings require using R code to work the examples. Those candidates that work through the examples or exercises will understand the material better than those who do not. The Time Series section (Section D) covers an introduction to modeling activity over time like financial results or stock prices using the Auto Regressive Integrated Moving Average (ARIMA) where activity in a given time period may be linked to activity in subsequent time periods. That connection between adjacent time periods violates one of the assumptions behind the Extended Linear Model techniques, but the ARIMA approach incorporates that linkage as an aid in predicting future results. The Time Series section also covers the application of regression models to time series analysis. A variety of tables will be provided to the candidate with the examination’s reference materials. The tables include values for the illustrative life tables, standard normal distribution, abridged inventories of discrete and continuous probability distributions, Chi-square Distribution, t-Distribution, and F-Distribution. Since they will be included with the examination, candidates will not be allowed to bring copies of the tables into the examination room. A guessing adjustment will be used in grading this exam. Details are provided under “Guessing Adjustment” in the “Examination Rules-The Examination” section of the Syllabus of Basic Education. Materials for Study, 2021 Exam MAS-I Exam MAS-I-2 SYLLABUS OF BASIC EDUCATION 2021 Modern Actuarial Statistics-I – Exam MAS-I A. Probability Models (Stochastic Processes and Survival Models) Range of weight for Section A: 20-35 percent Candidates should be able to solve problems using stochastic processes. They should be able to determine the probabilities and distributions associated with these processes. Specifically, candidates should be able to use a Poisson process in these applications. Survival models are simply an extension of the stochastic process probability models where one is estimating the future lifetime of an entity given assumptions on the distribution function used to describe the likelihood of survival. Markov Chains are a useful tool to model movement between states in a given process and underlie modern Bayesian MCMC models. A short section on computer simulation is included, since in some cases a closed form solution to a problem involving random variables is not possible and simulation provides a means to arrive at a solution. The Study Note will re-cast the generic survival model learning objectives to link those concepts to life actuarial symbols to help ensure P&C actuaries can communicate with life actuaries on basic concepts, but we should recognize that many disciplines like engineering or computer science incorporate survival models in their work. Life Contingencies problems can be viewed as discounted cash flow problems that can be set up and solved using Markov Chain concepts or simply viewed as three matrices in a spreadsheet indicating payment amount, likelihood of payment, and discount effect by time period as illustrated by Learning Objective A.7. LEARNING OBJECTIVES KNOWLEDGE STATEMENTS 1. Understand and apply the properties of Poisson a. Poisson process processes: b. Non-homogeneous Poisson process • For increments in the homogeneous case c. Memoryless property of Exponential and • For interval times in the homogeneous case Poisson • For increments in the non-homogeneous d. Relationship between Exponential and Gamma case e. Relationship between Exponential and Poisson • Resulting from special types of events in the Poisson process • Resulting from sums of independent Poisson processes Range of weight: 0-5 percent Materials

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