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Probability and Computational Finance Seminar
Daniel Schwarz Carnegie Mellon University Title: Integral representation of martingales motivated by the problem of market completion with derivative securities. Abstract: A model of a financial market is complete if any payoff can be obtained as the terminal value of a self-financing trading strategy. It is well known that numerous models, for example stochastic volatility models, are however incomplete. We present conditions, which, in a general diffusion framework, guarantee that in such cases the market of primitive assets enlarged with an appropriate number of traded derivative contracts is complete. From a purely mathematical point of view we prove an integral representation theorem which guarantees that every local Q-martingale can be represented as a stochastic integral with respect to the vector of primitive assets and derivative contracts. Date: Monday, April 28, 2014 Time: 5:00 pm Location: Wean Hall 8427 Submitted by: Dmitry Kramkov |