Theory and algorithms, simplex method, interior point methods, software packages for practical problem solving. Linear models in finance: the basic theorem of asset pricing, the pricing of financial derivatives in the arbitrage-free setting, use of linear programming for data classification, etc.
Condition for optimality, duality, interior point methods, software packages for practical problem solving. Financial models: various methods for creating and managing a portfolio, maximization of the Sharpe's ratio, mean-variance optimization, etc.
Overview of the theory and of the practical algorithms.
Financial models: minimal risk arbitrage, covariant matrix approximation, etc.
Use of stochastic models, modeling with uncertanity, methods for solving various stochastic prgramming problems. Examples in finance: portfolio building and management, risk averse optimization, etc.
Overview of the theory and of the basic methods for problem solving, dynamic programming in discrete and continuous time, continuous state space, optimal control. Examples in financial models: dynamic portfolio analysis, optimal stopping problem, etc.
The lecturer can also include other current topics from recent scientific periodicals in the course.
Since the content is of great practical importance we expect that also specialists from financial practice will present their work experience during the course.
Optimization in finance
D. P. Bertsekas, Dynamic programming and optimal control, Athena Scientific, 2005.
V. Chvátal: Linear Programming, Freeman, New York, 1983.
G. Cornuejols, R. Tütüncü: Optimization Methods in Finance, Cambridge Univ. Press, Cambridge, 2007.
A. Shapiro, D. Dentscheva, A. Ruszczynski: Lectures on Stochastic Programming:Modeling and Theory, MPS/SIAM Series on Optimization 9, SIAM, 2009.
S. Zenios: Financial Optimization, Cambridge Univ. Press, Cambridge, 1996.
Students acquire knowledge on the basic types of optimization problems, the stress being on the problems suitable for modeling problems coming from the field of finance. The students get acquainted with the basic mathematical approaches for solving the above optimization problems and use suitable software packages for solving practical problems.
With individual presentations and team work interactions within seminar/project activities students acquire communication and social competences for successful team work and knowledge transfer.
Knowledge and understanding:
The ability to describe various problems from the field of finance with a mathematical model. Knowledge on the basic approaches and software tools for efficient solving of the acquired optimization problems.
Solving more demanding practical optimization problems in finance.
The importance of presenting practical problems in formalized form which enables their efficient and correct solving.
Modeling the real-life problems in the form of a mathematical optimization problem, the ability to distinguish between computationally tractable and intractable problems, the ability to model and solve the problem on one's own using the computer.
Lectures, exercises, homeworks, consultations, seminars
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)
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