# Syllabus Math 565

## Math 565. Actuarial Models for Life Contingencies Instructor Syllabus

Text: David Dickson, Mary Hardy and Howard Waters. (2013). Actuarial Mathematics for Life Contingent Risks, Cambridge, Second Edition. (Chapters 7-10)

Introduction (3 hours)
Review Chapters 1-6 about the traditional actuarial models and theory of life contingencies

Chapter 7 – Policy Values (11 hours)

• Prospective loss random variables and (gross and net premium) policy values with traditional and general cash flows (4)
• Recursive and retrospective methods, Thiele’s differential equation and policy values at fraction age (4)
• Other topics related to policy values, including policy alterations, gain/loss analysis, asset share, deferred acquisition expenses and full preliminary term (3)

Chapter 8 – Multiple State Models (12 hours)

• Discrete-time Markov Chain and Markov multiple state models in discrete time (including the transition probability, Chapman-Kolmogorov equation, EPV of premiums/benefits) (4)
• Continuous-time multiple state models (including assumptions, probabilities, Kolmogorov’s forward equation, premiums and policy values) (4)
• Multiple decrement models (Multiple decrement table and the associated single decrement tables with fractional age assumptions) (4)

Chapter 9 – Joint Life and Last Survivor Benefits (9 hours)

• Distributional properties of the joint life and last survivor random variables (2)
• Insurance and annuity benefits for joint life and last survivor statuses (3)
• Multiple state models for multiple life analysis (3)
• The common shock model (1)

Chapter 10 – Pension Mathematics (6 hours)

• Introduction to pension mathematics (replacement ratio, the scale function, benefits, service table) (4)
• Defined benefit pension plans and defined contribution pension plans (2)

Midterm Exams (2 hours)
Total: 43 hours

Additional work required beyond the work required of undergraduates in the paired course:

Graduate students are expected to complete an extra research-oriented project or case study. A typical project involves reading and reporting on an academic paper or doing independent research on a relevant subject. A case study may require applications of theory and methodologies taught in class with substantial work on programming in software platforms such as R, Matlab or Python, etc.