Mathematical theories have been supplying economists with machineries for economic theory problems. Conversely, mathematicians have been stimulated by difficulties raised by these theories. This work aims to bring together mathematicians interested in getting new stimuli from the theories with economists who are seeking mathematical tools.

A lot of economic problems can formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who were seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking for effective mathematical tools for their researchers.

Takashi Adachi: Option on a unit-type closed-end investment fund.- Takahiko Fujita, Ryozo Miura: The distribution of continuous time rank processes.- Hirotaka Fushiya: Asymptotic expansion for a filtering problem and a short term rate model.- Elyes Jouini, Walter Schachermayer, and Nizar Touzi: Law invariant risk measures have the Fatou property.- Mikio Nakayama: The dawn of modern theory of games.- Manabu Toda: Approximation of excess demand on the boundary and equilibrium price set.- Yuji Umezawa: The minimal risk of hedging with a convex risk measure.- Na Zhang: The distribution of firm size.