Abstract:

The authors discussed a class of mathematical model of optimal investment theory. Such mathematical models can be attributed to a mixed initialboundary value problem of a parabolic MongeAmpère equation. We established the existence and uniqueness of classical solutions for the mixed initialboundary value problem of relevant equations using the continuity method combined with a prior estimates.

Key words: optimal investment theory, parabolic MongeAmpère equation, mixed initialboundary value problem