| CODE | SOR3430 | ||||||||
| TITLE | The Mathematics of Financial Markets: Discrete Models | ||||||||
| UM LEVEL | 03 - Years 2, 3, 4 in Modular Undergraduate Course | ||||||||
| MQF LEVEL | 6 | ||||||||
| ECTS CREDITS | 4 | ||||||||
| DEPARTMENT | Statistics and Operations Research | ||||||||
| DESCRIPTION | This study-unit provides an introduction to the mathematical modelling of asset prices, the consumption investment problem and the pricing of derivative securities. Single period models will be discussed first. The models will then be extended to cover the multiperiod (discrete) case. Study-unit Aims: Portfolio investment and derivative pricing amongst other problems are all based on having an adequate model for the asset prices. This study-unit aims at introducing students to the mathematical modelling of security prices, which has been and is still one of the major problems in the area of Financial Mathematics. Learning Outcomes: 1. Knowledge & Understanding By the end of the study-unit the student will be able to comprehend: - the dynamics of financial markets over single and multi-periods (discrete); - the deficiencies of such models and the need to generalize to a continuous setup; - the complex mathematical techniques used to devise proper mathematical models and to solve problems related to asset management. 2. Skills By the end of the study-unit the student will be able to: 1. analyze single period and multi-period financial market models, when the number of future possibilities is finite; 2. devise optimal portfolios and solve optimal consumption-investment problems for single period models by using the optimality conditions or the risk-neutral approach; 3. find optimal portfolios for multi-period models by using: - the optimality conditions - the risk-neutral approach - the method of dynamic programming. Main Text/s and any supplementary readings: - Pliska, S. (1997) Introduction to Mathematical Finance : Discrete Time Models, Blackwell. - Cvitanic, J., Zapatero, F. (2004) Introduction to the Economics and Mathematics of Financial Markets, MIT Press. - Hull, J C. (1993) Options, Futures, and Other Derivative Securities, Prentice Hall Inc. - Galitz , L. (1995) Financial Engineering, Pitman Publishing. - Wilmott, P., Howison, S. and Dewynne, J. (1999) The Mathematics of Financial Derivatives, Cambridge University. - Elliott, R.J., Kopp, P.E., (1999) Mathematics of Financial Markets, Springer. - Shreve, S.E. (2004) Stochastic Calculus for Finance II : Continuous time models, Springer. - Shreve, S.E. (2004) Stochastic Calculus for Finance I : The Binomial Asset Pricing Model, Springer. - Capinski, M., Zastawniak, T. (2003) Mathematics for Finance, Springer-Verlag. - Dupacova, J., Hurt, J., Stepan, J. (2002) Stochastic Modeling in Economics and Finance, Kluwer Academic Publishers. |
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| ADDITIONAL NOTES | Pre-requisite Study-units: SOR1110, SOR1450. |
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| STUDY-UNIT TYPE | Lecture, Independent Study & Tutorial | ||||||||
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| LECTURER/S | Mark A. Caruana |
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The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints. Units not attracting a sufficient number of registrations may be withdrawn without notice. It should be noted that all the information in the description above applies to study-units available during the academic year 2024/5. It may be subject to change in subsequent years. |
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