While absence of arbitrage in frictionless financial markets requires price processes to be
semimartingales, non-semimartingales can be used to model prices in an arbitrage-free …

In a numéraire-independent framework, we study a financial market with N assets which are
all treated in a symmetric way. We define the fundamental value∗ S of an asset S as its …

The classic approach to modeling financial markets consists of four steps. First, one fixes a
currency unit. Second, one describes in that unit the evolution of financial assets by a …

The present lecture notes are based on several advanced courses which I gave at the
University of Vienna between 2011 and 2013. In 2015 I gave a similar course (“Nachdiplom …

The discounted price process under the constant elasticity of variance (CEV) model is not a
martingale (wrt the risk-neutral measure) for options markets with upward sloping implied …

We pursue the robust approach to pricing and hedging in which no probability measure is
fixed, but call or put options with different maturities and strikes can be traded initially at their …

We construct and study market models admitting optimal arbitrage. We say that a model
admits optimal arbitrage if it is possible, in a zero-interest rate setting, starting with an initial …

Many results in stochastic analysis and mathematical finance involve local martingales.
However, specific examples of strict local martingales are rare and analytically often rather …

Die Arbeit gliedert sich in zwei Hauptteile. Der erste Teil ist eine theoretische Untersuchung
von Superhedging-Preisen und Finanzblasen in Marktmodellen mit proportionalen …

We consider implied volatilities in asset pricing models, where the discounted underlying is
a strict local martingale under the pricing measure. Our main result gives an asymptotic …