1. for ? ? ? a . Assumption 1 ensures that U is strictly quasi-concave. Together with the concavity of E(?), this implies the strict quasi-concavity of G, because G(?? 1 + (1 ? ?)? 2 ) > min{U (E(? 1 ), ? 1 ), U (E(? 2 ), ? 2 )} = min{G(? 1 ), G(? 2 )} a . It is well known that a strictly quasi-concave function ? ? G(?) is either strictly decreasing on;or it attains a unique maximum in ? * > ? a , while being strictly increasing on [? a , ? * ) and strictly decreasing on
2. Do Capital Adequacy Requirements reduce Risks in Banking?;J Blum;Journal of Banking and Finance,1999