Document Type
Syllabus
Publication Date
Fall 9-1-2024
Course Description
Probability theory constitutes a core section of actuarial mathematics. In fact, probability permeates most analyses in the world of actuarial science. Certainly, probability theory is used as a foundation for analyzing and evaluating the financial costs of risk and uncertainty. Actuaries help their companies and clients develop strategies to minimize risk and manage costs utilizing probability theory. Any analysis of risk and risk theory is an expansion of mathematical probability. Furthermore, all statistical inference is rooted in probability theory. For actuaries to have a clear understanding of any advanced statistical analysis or the varied statistical tools available to them to help solve business problems, they need a strong foundation in probability theory. Example of Probability Theory Application on the Job Rafael works for a large insurer where his responsibilities include building predictive models to help determine the risk of hurricanes. Those predictive models are used to help determine a reasonable amount to charge for that hurricane risk in the insurance products his company sells. He first uses his knowledge of statistical distributions to select a curve that best fits his company’s hurricane severity data. From there, he may choose to credibility weight that curve with a curve based on industry data. The combined curve could be used to determine the relationship between how severe a storm is and the probability of that storm occurring. Rafael can interpolate to get smoothed values or extrapolate to understand what could be happening in extreme situations. Rafael might calculate the severity of the 99th percentile hurricane to determine what type of catastrophe load should be built into the price of a product. To be more conservative, he might instead calculate the average severity of a hurricane given that it is worse than the 99th percentile. Without Rafael’s strong understanding of probability theory, his company may set the price of a product too low and then won’t have generated enough revenue to cover losses when a hurricane strikes. Conversely, if the risk is over-estimated, the price of the product might be set too high and no longer be competitive in the marketplace. Course Description: Part I: Topics of Risk and Insurance are not covered in Math 441 which mainly helps students build the general background and theoretical foundation of Probability. Details are Order statistics, Law of large numbers, basic insurance policies, frequency of loss, frequency distribution, severity, severity distribution, the expected value of the loss, loss distribution, premium payment, claim payment distribution, limits on policy benefit (deductible, maximum, benefit limits) and role of actuaries. Part II: Problem sets. A problem set consisting of 30-35 problems is assigned after we finish each chapter in Math 441. The difficulty level of the problems is similar to the real exam. The problems discussed in the seminars provide students with a better understanding of the actuarial field by exposing students to professional applications of actuarial science and by providing resources for students taking actuarial exams. By the end of this semester, several sets of practice of exams will be distributed for practicing Exam P. Each practice exam should be finished in three hours.
Recommended Citation
Wu, Zhixin, "MATH 442 Probability Problem Seminar Wu Fall 2024" (2024). All Course Syllabi. 952, Scholarly and Creative Work from DePauw University.
https://scholarship.depauw.edu/records_syllabi/952
Student Outcomes
After students complete this course, they will demonstrate the ability to: 1. Understand the insurance and risk management topics that use probability theories. 2. Understand the probability application in insurance and risk management, or related fields. 3. Master the learning strategies and techniques to meet the expectation of the actuarial professional exams 4. Master the strategies and techniques to find internship and succeed in job interviews.