Bergische Universität Wuppertal Fachbereich Mathematik und Naturwissenschaften Angewandte Mathematik - Numerische Analysis (AMNA)

People Research Publications Teaching

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The lecture is suitable for students of mathematics as well as for economics.
The students of economathematics can use it as component AKap.NAaA-a "Selected Topics in Numerical Analysis and Algorithms" in the module of the same name.

Topics of the Lecture:

1. Convex extensions of the Markowitz portfolio selection problem
2. Risk measures and decision models
3. Hamilton-Jacobi-Bellman equation for dynamic portfolio optimization problems

Literature:

• S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, March 2004.
• G.Ch. Pflug and W. Römisch, Modeling, Measuring and Managing Risk, World Scientific Pub Co Inc, April 2008.
• S. Kilianova and D. Sevcovic, A Transformation Method for Solving the Hamilton-Jacobi-Bellman Equation for a Constrained Dynamic Stochastic Optimal Allocation Problem, ANZIAM Journal (55) 2013, 14-38.
• S. Kilianova and D. Sevcovic, Dynamic intertemporal utility optimization by means of Riccati transformation of Hamilton-Jacobi Bellman equation, Japan Journal of Industrial and Applied Mathematics, 36(2) 2019, 497-517.

Previous knowledge: Analysis I - III, basic knowledge of ordinary differential equations.

Exercises: Übungsblätter, Materialien

Criteria: Regular participation and participation in the exercise groups, as well as reaching 50% of the possible points on the first seven or the remaining exercise sheets and at least 2/3 of the possible points for the practical tasks.