Abstracts

In mathematical finance a model of a financial market is said to be complete if any payoff can be obtained as the terminal value of a self-financing trading strategy. The completeness property is important because it allows the hedging of any non-traded derivative security. Yet, numerous models, such as stochastic volatility models or structural models in commodity markets are incomplete. We present conditions, in a general diffusion framework, which guarantee that in such cases the market of primitive assets enlarged with an appropriate number of traded derivative contracts is complete. Key to the proof is the analyticity in time and space of the coefficients of the model, allowing us to draw upon recent results on the analytic smoothing properties of linear parabolic partial differential equations.