Department Mathematik



Mathematisches Kolloquium

Am Donnerstag, 12. März 2009, um 11 Uhr s.t. spricht

Dr. Mark Oliver Rieger
(Universität Zürich)

im Hörsaal B132 über das Thema

Two applications of transport theory: fracture in "elastic" materials and optimization of financial products

Zusammenfassung: In the first part of my talk I present results on a model for fracture in a material, based on gradient flows of Young measures and methods from transport theory. The model gives a unified description of elastic behavior, damage and fracture. Mathematically similar ideas can be applied in a very different field, namely in financial methematics of more precisely in the optimization of financial products. In the second part of my talk I will explain this connection and prove that under very weak conditions optimal financial products on complete markets are co-monotone with the inverted state price density. In most cases, this implies that the payoff of an optimal financial product can simply be written as a monotone function of the market portfolio. Applications of this result will be outlined.