This module aims to equip students with skills to enable them to mathematically model and analyse real life events. They will also be able to use different CFD techniques, numerical analysis and data structures to solve problems that involve fluid flow. With reference to competence-based curriculum (CBC), students will be equipped with knowledge of the Navier-Stokes equations the fundamental basis of almost all CFD problems which define many single-phase fluid flows. Turbulence flow will be the application.
The current module for 10 credits seeks to equip students with skills in continuous time finance. The indicative contents include: General probability theory, information on conditioning, Brownian motion, Stochastic calculus, Risk-neutral pricing, Connection with partial differential equations, some applications in
1) American derivative securities,
2) Change of Numeraire,
3) Term structure models
The current module seeks to equip students with advanced skills in risks analysis for insurance industry. Indicative content include
1) Probability distributions and insurance application
2) Utility theory
3) Principles of premium calculation
4) The collective risk model
5) The individual risk model
6) Introduction to ruin model
7) Classical ruin theory
8) Advance ruin theory
9) Reinsurance
References
1. David C. M. Dickson, Insurance Risk and Ruin, (International series on actuarial science), Cambridge University Press, the Edinburgh Building, Cambridge CB2 2RU, UK, 2005.
2. Alexander Melnikov, Risk analysis in Finance and Insurance, Chapman and Hall/CRC, London, 2004
This module aims at providing students with the general techniques needed to analyse mathematical models in biology. It introduces dynamical mathematical models in terms of ordinary differential equations using population dynamics, age-structured population and infectious and chronic disease as case studies. The module presents models biochemical reaction networks and reaction diffusion, chemotaxis, stochastic modeling of population growth. The students will be provided with the general techniques to compute the solution numerically with the aid of a computer.