The effects of small tansaction costs on investment strategies and their efficiency

• Applicant: Professor Dr. Jan Kallsen
• Subject Area: Mathematics
• Term: from 2013 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 248598775

Classical models of financial markets typically involve the bid-ask spread of asset prices. Transactions costs and taxes do not only complicate the mathematical treatment of many quantitative issues considerably, they also lead to different qualitative behaviour. As a way out, the asmyptotics for small transaction costs has received increasing attention. It allows to study the effects of such market frictions even in quite complex models and to quantify them to the leading order. The proposed project is based directly on this recent research. Some general results in the literature are derived using purely formal arguments. A main goal is to rigorously prove these statements under precise and verifiable assumptions. Moreover, the results shall be generalised to the more involved, but also practically more relevant case of multiple traded assets. Finally, proportional transaction costs shall be replaced with alternative structures, which are only partly understood so far. This includes fixed fees, which are dominating for small investors, as well as liquidity effects, which are relevant for large market participants.

• DFG Programme: Research Grants