Abstract: For the initial value problem of a parabolic Monge-Ampère equation: V_sV_yy+ryV_yV_yy-θV²_{y< /sub>=0, Vyy<0, (s,y)∈［0,T)×R; V(T,y)=1-e^-λy, y∈R. arisen from optimal investment theory in mathematical finance, the existence an d the uniqueness as well as the application of the solution V=V(s,y) are established.}

Key words: parabolic Monge-Ampère equation, initial value problem, unbounded initial value, optimal investment