Fractional regularity and stochastic analysis of discretizations; Adaptive simulation algorithm in credit risk

Abstract : This thesis deals with three issues from numerical probability and mathematical finance. First, we study the L2-time regularity modulus of the Z-component of a Markovian BSDE with Lipschitz-continuous coefficients, but with irregular terminal function g. This modulus is linked to the approximation error of the Euler scheme. We show, in an optimal way, that the order of convergence is explicitly connected to the fractional regularity of g. Second, we propose a sequential Monte-Carlo method in order to efficiently compute the price of a CDO tranche, based on sequential control variates. The recoveries are supposed to be i.i.d. random variables. Third, we analyze the tracking error related to the Delta-Gamma hedging strategy. The fractional regularity of the payoff function plays a crucial role in the choice of the trading dates, in order to achieve optimal rates of convergence.
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Mathematics [math]. Institut National Polytechnique de Grenoble - INPG, 2009. English


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Submitted on : Friday, February 26, 2010 - 3:46:28 PM
Last modification on : Saturday, January 26, 2013 - 8:38:11 PM

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Azmi Makhlouf. Fractional regularity and stochastic analysis of discretizations; Adaptive simulation algorithm in credit risk. Mathematics [math]. Institut National Polytechnique de Grenoble - INPG, 2009. English. <tel-00460269>

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