Lesson 1: The Ramsey growth model in economic theory

Lesson 2: Solving the Hamilton-Jacobi equation

Lesson 3: Intergenerational equity, time inconsistency and equilibrium strategies

Lesson 4: Soving systems of Hamilton-Jacobi equations

• WK student seminar

• WK student seminar

• WK student seminar

• WK student seminar

• WK student seminar

• WK student seminar

• WK student seminar

• WK student seminar

• WK student seminar

• WK student seminar

• WK student seminar

• WK student seminar

• WK student seminar

• WK student seminar

Abstract: Periodic irrotational traveling water waves are known to be smooth, with exception of the largest possible wave which has a corner at the wave crest (the lateral tangents being at an angle of 2\pi/3). Is the regularity of waves of small and moderate amplitude destroyed by vorticity? This is joint work with J. Escher.

• Event: 10. Pauli Kolloquium (2010)

Abstract: I show that first order symmetric hyperbolic systems in three space and one time variable always have multiple characteristics if the order n of the system is congruent 2 mod 4, n = 2, 6, 10, etc. The proof has a topological flavour and leads to an interesting algebraic problem.

• Event: 10. Pauli Kolloquium (2010)

We consider Composite Piezoelectric Cantilever and in order to stabilize this system, passivity based feedback control has been applied. The asymptotic stability of the closed-loop error system is proven using semigroup theory and LaSalle´s invariance principle. Moreover, we discuss exponential stability and show that the system is not exponentially stable.

• WK student seminar

We will start with a short introduction to a new model for mulitmode lasing systems. Within this approach the key simulation reduces to a full space Helmholtz EVP. Then we will discuss the numerical computation exploiting the FEM-Code of Joachim Schöberl. Finally we give an outlook on further collabortations with physisists from the institut of theoretical physics at the Vienna University of Technology.

• WK student seminar

In this work, we investigate the dynamics of a modified Keller-Segel type model. On the contrary to the classical configuration, the chemical production term is located on the boundary. In the one-dimensional case and in a particular case in dimension two, we prove, under suitable assumptions, the following dichotomy which is reminiscent of the two-dimensional Keller-Segel system. Solutions are global if the mass is below the critical mass and they blow-up in finite time above the critical mass. Furthermore, in the one-dimensional case, using entropy techniques, we provide quantitative convergence results for the subcritical case. This work is completed with a more realistic model (still one-dimensional) for modeling purpose. In this new setting, the chemical is supplied by a quantity which evolves by exchanging particles at the boundary.
Finally some results are given for the two-dimensional case and we also provide some links with cell polarisation that is an essential step for many biological processes and that is involved for instance in cell migration, division, or morphogenesis.

• Thematic program: Cell movement and cell transport (CELL-09) (2009)
• WK seminar

Steady transonic flows through channels so narrow that the classical boundary layer approach fails are considered. The resulting viscous inviscid interaction problem for weakly three dimensional laminar flows is formulated for perfect gases under the requirement that the channel is sufficiently narrow so that the flow outside the viscous wall layers becomes two-dimensional in the leading order approximation. The behavior of the flow upstream of a surface mounted three-dimensional obstacle will be demonstrated.

• WK student seminar

First, we will give an introduction to fast-slow systems. The geometric viewpoint of the theory will be emphasized. Then we discuss the three-dimensional FitzHugh-Nagumo (FHN) equation and its bifurcations. The singular limit bifurcation diagram of the FHN equation will be derived. We shall also look at mixed-mode oscillations (MMOs) in the FHN equation and outline the role of MMOs in chemistry, neuroscience and physics.

• WK seminar

We show that the compensation for rare events accounts for a large fraction of the average equity and variance risk premia. As such, our results suggest that any satisfactory equilibrium-based asset pricing model must be able to generate both large and time-varying compensations for fears of disasters. Our empirical investigations are essentially model-free, involving new extreme value theory approximations based on ``medium'' size jumps in high-frequency intraday prices for estimating the expected values of the tails under the statistical probability measure, and short maturity out-of-the money options and new model-free implied variation measures for estimating the corresponding risk neutral expectations.

• Event: Working Group "The interplay between Financial and Insurance Mathematics, Statistics and Econometrics" (2010)

In the context of high frequency data, like financial data, many questions have been solved in the recent years. But of course there are still many open problems, and we will review a few of those. This review will include specific problems like the estimation of the volatility when there are high activity jumps, and more general questions like the choice of appropriate models.

• Event: Working Group "The interplay between Financial and Insurance Mathematics, Statistics and Econometrics" (2010)