ETH Zurich

An investor trades a safe and several risky assets with linear price impact to maximize expected utility from terminal wealth.

In the limit for small impact costs, we explicitly determine the optimal policy and welfare, in a general Markovian setting allowing for stochastic market,

cost, and preference parameters. These results shed light on the general structure of the problem at hand, and also unveil close connections to

optimal execution problems and to other market frictions such as proportional and fixed transaction costs.

We discuss a simple variational principle for coherent material vortices

in two-dimensional turbulence. Vortex boundaries are sought as closed

stationary curves of the averaged Lagrangian strain. We find that

solutions to this problem are mathematically equivalent to photon spheres

around black holes in cosmology. The fluidic photon spheres satisfy

explicit differential equations whose outermost limit cycles are optimal

Lagrangian vortex boundaries. As an application, we uncover super-coherent

material eddies in the South Atlantic, which yield specific Lagrangian

transport estimates for Agulhas rings. We also describe briefly coherent

Lagrangian vortex detection to three-dimensional flows.