摘要

Our main topic in this article is the forward utility field, which is a quite a new concept introduced by Musiela and Zariphopoulou. Different from most article in this field discussing forward utility in a continuous market, we extend this concept to jump market case. We first provide a generalized Ito-Ventzell formula, which can be applied in a general jump semimartingale driven by Brownian motion and Poisson random measure. Then three special forward utility models are discussed by exploiting this generalized Ito-Ventzell formula.

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