ESB: Game options and markets with frictions

Financial mathematics became an important part of probability theory with influential applications for understanding the dynamics of financial markets. Berlin became one of the world centers of financial mathematics with Prof. P. Imkeller and Prof. P. Bank being among the leaders in the field. Hebrew University is also becoming a center of financial mathematics with Prof. Y. Kifer who introduced in 2000 the now prominent and widely studied notion of game (Israeli) options and his former student Dr. Y. Dolinsky, now senior lecturer at Hebrew University. Game options allow cancellation by their issuers leading to a reduction of their risk - an appealing feature in the current state of instability of financial markets. An important part of the proposed research is a comprehensive study of various aspects of game options. Specifically, we plan to investigate how techniques of backward stochastic differential equations can be brought to bear on the valuation problem for these options in incomplete markets, most notably in terms of utility indifference pricing. Such techniques have been spearheaded by P. Imkeller who also contributed to our understanding of asymmetric information issues which we now plan to investigate in the context of Kifer's game options. Another important topic for game options in our program is to obtain suitable stochastic representations of the type of running maxima. For American options this was achieved by P. Bank in collaboration with H. Föllmer and N. El Karoui. It will provide a novel approach to the game options' optimal exercise problem. We also propose to study the super replication problem of American and game options in various models of illiquidity. These are related to works of P. Bank on markets with a large trader and of Y. Dolinsky on markets with frictions. Y. Dolinski's expertise for asymptotic results between discrete and continuous-time models of financial markets will be of central importance for our program. This proposal brings together specialists from Hebrew University with Berlin's Humboldt-Universität and Technische Universität, making the Einstein foundation the ideal framework for this project.