Problems arising in Finance have become a significant source of new developments in Stochastic Analysis. We discuss some recent case studies, in particular some decomposition and representation theorems which are motivated by problems of hedging derivatives and of intertemporal consumption choice.

"Je höher man steigt, umso tiefer der Fall" - auf wohl kein Phänomen trifft dieser Ausspruch so gut zu wie auf Finanzkrisen. Steigen die Preise für ein Spekulationsobjekt in immer gröe︢re Höhen und erhitzt sich der Markt immer mehr, ist die Folge meist ein abrupter Fall: Die Blase platzt!...

A primary goal in modelling the dynamics of implied volatility surfaces (IVS) aims at reducing complexity. For this purpose one fits the IVS each day and applies a principal component analysis using a functional norm. This approach, however, neglects the degenerated string structure of the...

The economic theory of option pricing imposes constraints on the structure of call functions and state price densities (SPDs). Except in a few polar cases, it does not prescribe functional forms. This paper proposes a nonparametric estimator of option pricing models which incorporates various...

This paper is devoted to the problem of hedging contingent claims in the framework of a complete two-factor jump-diffusion model. In this context, it is well understood that every contingent claim can be hedged perfectly if one invests the unique arbitrage-free price. Based on the results of H....