An initial-boundary value problem for parabolic Monge-Ampère equation in mathematical finance

Abstract

This paper deals with some parabolic Monge-Ampère equation raised from mathematical finance: V _s V _yy+ry V _y V _yy−θV _y ²= 0 (V _yy < 0). The existence and uniqueness of smooth solution to its initial-boundary value problem with some requirement is obtained.

Keywords

Initial-boundary value problem / Parabolic Monge-Amp`ere equation / Strong convex monotonic function

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