Year
2011

Johannes took his PhD in mathematics under the supervision of Jan Kallsen at TU Muenchen, in April 2009, with his thesis on "Shadow Prices in Portfolio Optimization with Transaction Costs".
The ceremony was held at Politecnico di Milano, at the presence of the Nicola Bruti Liberati family (the parents - in the picture), the Politecnico di Milano representatives (Emilio Barucci, Sandro Salsa and Piercesare Secchi), and Springer Italia (Francesca Bonadei, responsible Editor).