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Module Title |
Stochastic Modelling
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Module Code |
MS308
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School |
School of Mathematical Sciences
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Online Module Resources
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Level |
3
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Credit Rating |
7.5
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Pre-requisite |
None
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Co-requisite |
None
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Module Aims
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To give a comprehensive introduction to the Stochastic Processes and their application to Actuarial Science
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Learning Outcomes
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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.
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Indicative Time Allowances
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Hours
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Lectures |
36
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Tutorials |
12
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Laboratories |
0
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Seminars |
0
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Independent Learning Time |
64.5
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Total |
112.5
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Placements |
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Assignments |
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NOTE
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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.
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Indicative Syllabus
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STOCHASTIC MODELLING: review of basic probabilistic concepts, the various types of stochastic processes, stationarity, Markov processes, the Chapman-Kolmogorov equation, stationary probability distributions.
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.
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; survival models, sickness and death, estimation of transition rates.
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| Assessment | | Continuous Assessment | 25% | Examination Weight | 75% |
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Indicative Reading List
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Essential
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., NewYork Academic Press, 1975.
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Programme or List of Programmes
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| BSSA | Study Abroad (DCU Business School) |
| BSSAO | Study Abroad (DCU Business School) |
| ECSA | Study Abroad (Engineering & Computing) |
| ECSAO | Study Abroad (Engineering & Computing) |
| FM | BSc in Financial & Actuarial Mathematics |
| GCAS | Grad Certificate in Actuarial Science |
| HMSA | Study Abroad (Humanities & Soc Science) |
| HMSAO | Study Abroad (Humanities & Soc Science) |
| MS | BSc in Mathematical Sciences |
| SHSA | Study Abroad (Science & Health) |
| SHSAO | Study Abroad (Science & Health) |
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