In an incomplete market framework, contingent claims are of particular interest since they improve the market efficiency. This paper addresses the problem of market completeness when trading in contingent claims is allowed. We extend recent results by Bajeux and Rochet (1996) in a stochastic volatility model to the case where the asset price and its volatility variations are correlated. We also relate the ability of a given contingent claim to complete the market to the convexity of its price function in the current asset price. This allows us to state our results for general contingent claims by examining the convexity of their "admissible arbitrage prices." Copyright Blackwell Publishers Inc 1997.

We present several results and methods concerning the convergence of numerical schemes for problems arising in Finance theory. This paper is essentially expository but we present however new results concerning some problems of rate of convergence.

We study the critical price of an American put option near expiration in the Black-Scholes model. Our main result is an estimate for the difference &Pmacr; ("t")- "K" between the critical price at time "t" and the exercise price as "t" approaches the maturity of the option. Copyright 1995 Blackwell Publishers.