The main objective of the course is to bridge the gaps between the elementary probability theory and the excellent works on advanced probability theory.

The course will also provide the students with grounding in stochastic processes and survival methods and their application.

It will also prepare the students to sit for the professional examinations in actuarial science conducted by renowned professional actuarial bodies such as Institute and Faculty of Actuaries, UK and Society of Actuaries, USA.

discuss and understand when it is appropriate to use probability generating function

describe the general principles of stochastic processes and their classification

define a Markov chain and a Markov process

understand and describe the principles of actuarial modeling

explain the concept of survival models

understand and describe estimation procedures for lifetime distribution

describe how to test crude estimates for consistency with a standard table or a set of graduated estimates

sit for the actuarial professional examinations in relevant course paper of actuarial science

Generating Function: Basic Concept, Convolution, Bivariate generating function, Continuity Theorem

Limit Theorem: Mutual independence of random variables, Convergence of sequence of random variables

Random Walk and Ruin Problem: Classical Ruin problem, Expected duration of game, Generating functions for duration for duration of game and for first passage time

Markov Chain: Features of a Markov chain model, Chapman-Kolmogorov equations, Time in homogeneous Markov chain model, Use of Markov chain as a tool for modeling and simulation

Markov Process: Features of a Markov process model, Kolmogorov equations for a Markov process, Survival models, sickness models and marriage models in terms of Markov processes, Use of Markov jump processes as a tool for modeling and simulation

Homogeneous Markov Processes: Poisson process, Simple birth process, Simple death process, Simple birth–death process, Effect of immigration. Queuing process, Single server queues, Equilibrium theory, Queues with many servers, Limiting properties of queues.

Point Process: Stationary point process, Renewal process, Doubly stochastic process.

Branching Process: Structure of process, Age dependent branching process, Branching renewal process.

Methods of graduation: parametric formulae, standard table, graphical representation

Principles of Actuarial Modeling: Basic concept of actuarial model, Benefits and limitations of modeling, Difference between stochastic and deterministic model, Short-run and long-run properties of a model, Process of sensitivity testing of assumptions

1)

Actuarial Education Company, United Kingdom, CT4 Models Core Technical, [Gupta, Promislow, Kass ]

2)

Gikhman, I.I., A.V. Skorokhod (2004). The Theory of Stochastic Processes, Springer. [Process I, Process II, Process III, Bowers]

3)

Cox and Miller (1985). The theory of Stochastic Process. [Medhi, Ross]

4)

Krishnan, V. (2006). Probability and Random Processes, Vol. 3. John Wiley & Sons

5)

Lund, R.B. (2003). Elements of Applied Stochastic Process. Journal of the America Statistical Association, 98(464). [Feldman]

6)

Srinivasan, S.K. ,S A. Vijayakumar (2003). Stochastic Point Processes. Alpha Science Int’l Ltd. [Daley]