The p-optimal martingale measure in continuous trading models

Abstract

We discuss the p-optimal martingale measure for p∈(1,∞) in continuous incomplete markets whose stock price is fluctuated by a d-dimensional continuous semimartingale. In this paper, we treat two simple models. One is a model where the mean-variance trade-off process is deterministic. Another is a model where the minimal martingale measure coincides with the minimal entropy martingale measure. In these models, we prove that the p-optimal martingale measure coincides with the minimal martingale measure under some conditions.