一个来自投资理论的抛物型Monge-Ampère方程初值问题

AN INITIAL VALUE PROBLEM FOR A PARABOLIC MONGE-AMPMERE EQUATION FROM INVESTMENT THEORY

为寻找抛物型Monge-Ampere方程的初值问题VsVyy+ryVyVyy-θV2y=0, Vyy<0,(s,y)∈[0,T)×R, V(T,Y)=g(y), g'(y)≥0,Y ∈R 满足最优投资理论要求的解,本文给出一个途径,并得到某些存在性结果.

For finding solutions satisfying requirement from optimal investment theory to the initial value problem for a parabolic Monge-Ampmere equation: VsVyy+ ryVyVyy-θV2y =0. Vyy< 0,(s, y) ∈[0, T)×R. V(T,y)=g(y). g'(y) ≥0, y ∈ R, an approach is given, and some results about the existence are obtained.