# Actuarial Mathematics

Course TypeCourse CodeNo. Of Credits
Foundation ElectiveSUS1MA517/5374

Semester and Year Offered: Winter semester

Course Coordinator and Team: Geetha Venkataraman and others

Email of course coordinator: geetha[at]aud[dot]ac[dot]in

Pre-requisites: Mathematics at the XII grade level and 4 credits each of SUS1MA507 (Probability and Statistics) and SUS1MA536 (Mathematical Finance)

Aim:

This Course is primarily intended for students interested in Statistics and Actuarial Science. This course will be beneficial not only for Mathematics Programme students but also for the students of other disciplines. This is an introductory course on Actuarial Mathematics and also has applications.

Course Outcomes:

After completing this course students will be able to

1. understand and identify concepts of deterministic models, stochastic processes, life table, survival distributions and failure times.
2. calculate and apply to real life concepts emanating from above.
3. get a base, required for getting certified as actuary.

Brief description of modules/ Main modules:

The basic deterministic model: Cash flows, Analogy with currencies, Discount functions and its calculation, interest and discount rates, Constant interest, values and actuarial equivalence, Regular Pattern cash flows, Balance and Reserves and its relationship, Prospective versus retrospective methods, Recursion formulas, Time shifting and the splitting identity, change of discount function

introduction to stochastic processes: Introduction, Markov Chains, Martingales, Finite State Markov chains. Poisson Process, waiting times, Properties of Poisson Process, Non-Homogeneous Poisson process, Compound Poisson Process.

Life table: Basic definitions, probabilities, constructing life tables from values of qx, Life expectancy, construction of life table

Survival distributions and failure times: Introduction to survival distributions, The discrete case, The continuous case, The Gompertz–Makeham distribution, shifted distributions, The standard approximations, Stochastic Life table, Life expectancy in the stochastic model, Stochastic interest rates.

Assessment Details with weights:

 S. No. Assessment Date/period in which Assessment will take place Weightage 1 Class test First week of February 10% 2 Mid Semester Exam Early March 25% 3 Home Assignments/ Tutorials Throughout the semester 15% 4 Presentation/ Viva Early April 15% 5 End Semester Exam End April-early May 35%