Incomplete markets: Convergence of options values under the minimal martingale measure

摘要

In the setting of incomplete markets, this paper presents a general result of convergence for derivative assets prices. It is proved that the minimal martingale measure first introduced by Follmer and Schweizer is a convenient tool for the stability under convergence. This extends previous well-known results when the markets are complete: both in discrete time and continuous time. Taking into account the structure of stock prices, a mild assumption is made. It implies the joint convergence of thr sequences of stock prices and of the Radon-Nikodym derivative of the minimal measure. The convergence of the derivatives prices follows. This property is illustrated in the main classes of financial market models. AMS 1991 Subject Classification: Primary 60F05; 60G35; 90A09. [References: 31]