Registry

Module Specifications

Archived Version 2008 - 2009

Module Title	Stochastic Modelling
Module Code	MS308
School	School of Mathematical Sciences
Online Module Resources
Level	3	Credit Rating	7.5
Pre-requisite	None
Co-requisite	None

Module Aims

To give a comprehensive introduction to the Stochastic Processes and their application to Actuarial Science.

Learning Outcomes

As a result of this module the students will have a good understanding of the most important properties of Markov chains and Markov jump processes. They will gain experience of these tools for modelling in Actuarial Science.

Indicative Time Allowances
	Hours
Lectures	36
Tutorials	12
Laboratories	0
Seminars	0
Independent Learning Time	64.5

Total	112.5
Placements
Assignments

NOTE

Assume that a 7.5 credit module load represents approximately 112.5 hours' work, which includes all teaching, in-course assignments, laboratory work or other specialised training and an estimated private learning time associated with the module.

Indicative Syllabus

Stochastic Modelling: Review of basic probabilistic concepts, the various types of stochastic processes, stationarity, Markov processes, the Chapman-Kolmogorov equation, stationary probability distributions. [CT4 - (ii)]

Markov Chains: Solution of the Chapman-Kolmogorov equation in matrix form, transition graph, finding the stationary distribution, actuarial examples; two-state chains; the limiting distribution of finite Markov chains, irreducibility and aperiodicity, exponential convergence; infinite Markov chains, criteria for recurrence, the limiting distribution and its relation to mean recurrence times; applications: queues, random walks with various boundary conditions. [CT4 - (iii)]

Markov Jump Processes: The infinitesimal generator, the forward and backward equations, solution in exponential form; holding times, exponential distribution, jump chain; the limiting distribution of a finite Markov jump process and its connection to mean recurrence times; the case of infinite state spaces, the integral form of the backward equation, the minimal process, conservative processes; the Poisson process and actuarial models; inhomogeneous Markov jump processes, time-dependent transition rates, the backward equation in differential and integral forms, residual holding times. [CT4 - (iv)]

Survival models, sickness and death, estimation of transition rates; finite population observed fora fixed time interval, truncated life-times, unbiased estimator of transition rate, asymptomatic distribution, poisson approximation. [CT4 - (vii)]

Assessment
Continuous Assessment	25%	Examination Weight	75%

Indicative Reading List

Acted material for CT4 subject ‘models’.
Bhattacharya, R.N., and Waymire R.C., Stochastic Processes with Applications, New-York, Wiley, 1990.
Grimmett, G.R. and Stirzaker, D.R., Probability and Random Processes, 2dn ed. Oxford University Press, 1992.
Karlin, S. and Taylor, H.M., A First course in Stochastic Processes, 2nd ed., New York Academic Press, 1975.
Norris, J.R., Markov Chains, Cambridge University Press, 1997.

Programme or List of Programmes

BSSA

Study Abroad (DCU Business School)

BSSAO

Study Abroad (DCU Business School)

ECSA

Study Abroad (Engineering & Computing)

ECSAO

Study Abroad (Engineering & Computing)

BSc in Financial & Actuarial Mathematics

HMSA

Study Abroad (Humanities & Soc Science)