Obiettivo The recent financial crisis has brought to light the importance of correctly evaluating financial assets and their underlying risk. Any such valuation should be robust, i.e. should not be overly sensitive to the modelling assumptions. According to the Black--Scholes theory, which lies at the heart of most current valuation methods, the risk involved by a financial asset can be perfectly eliminated by pursuing a proper dynamic hedging strategy. Unfortunately, although formally elegant, this theory is too much of an idealization of the real world situation. The underlying model fails to be robust in two ways: the prices follow geometric Brownian motion, and transaction costs must be zero. The use of alternative models, e.g. based on fractional Brownian motion, was proposed more than 45 years ago by B.~Mandelbrot. The empirical findings give support to the use of such alternative models. Nevertheless, up to now these models could not be used to value financial assets, as they are not free of arbitrage. We propose an approach which makes it possible to value financial assets in an arbitrage free way, even in the framework of fractal models, by properly taking transaction costs into account. Our approach is based on utility theory. We also propose to control the risk of the related hedging strategies by imposing bounds in terms of risk measures. This allows for more realistic financial modelling with special emphasis on the aspect of the residual risk, remaining after hedging. From a mathematical point of view, our approach is based on the duality theory of infinite-dimensional optimization. Programma(i) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Argomento(i) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations Invito a presentare proposte ERC-2009-AdG Vedi altri progetti per questo bando Meccanismo di finanziamento ERC-AG - ERC Advanced Grant Istituzione ospitante UNIVERSITAT WIEN Contributo UE € 1 266 000,00 Indirizzo UNIVERSITATSRING 1 1010 Wien Austria Mostra sulla mappa Regione Ostösterreich Wien Wien Tipo di attività Higher or Secondary Education Establishments Ricercatore principale Walter Schachermayer (Prof.) Contatto amministrativo Helmut Schaschl (Dr.) Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Costo totale Nessun dato Beneficiari (1) Classifica in ordine alfabetico Classifica per Contributo UE Espandi tutto Riduci tutto UNIVERSITAT WIEN Austria Contributo UE € 1 266 000,00 Indirizzo UNIVERSITATSRING 1 1010 Wien Mostra sulla mappa Regione Ostösterreich Wien Wien Tipo di attività Higher or Secondary Education Establishments Ricercatore principale Walter Schachermayer (Prof.) Contatto amministrativo Helmut Schaschl (Dr.) Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Costo totale Nessun dato
