... and Pontryagin’sprinciple of optimality [Zelkina], but except for the entry of Brock–Dechert, in each of these it turns up in a passing and cursory way. And, in anothersearch engine, extensive ... behind Debreu’s the-ory was that the individual demands of consumers are continuously differ-entiable. The mathematical model that appears in this case is a system ofequations involving continuously ... would incur some shortfall risk. Hence, fixing the limit of her shortfallS. Kusuoka, T. Maruyama (eds.), Advances in Mathematical Economics Volume 14,1DOI: 10.1007/978-4-431-53883-7 1,c Springer...