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A Generalized MeanReverting Equation and Applications
 ESAIM:PS
"... Abstract. Consider a meanreverting equation, generalized in the sense it is driven by a 1dimensional centered Gaussian process with Hölder continuous paths on [0, T] (T> 0). Taking that equation in rough paths sense only gives local existence of the solution because the nonexplosion condition ..."
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Abstract. Consider a meanreverting equation, generalized in the sense it is driven by a 1dimensional centered Gaussian process with Hölder continuous paths on [0, T] (T> 0). Taking that equation in rough paths sense only gives local existence of the solution because the nonexplosion condition is not satisfied in general. Under natural assumptions, by using specific methods, we show the global existence and uniqueness of the solution, its integrability, the continuity and differentiability of the associated Itô map, and we provide an Lpconverging approximation with a rate of convergence (p> 1). The regularity of the Itô map ensures a large deviation principle, and the existence of a density with respect to Lebesgue’s measure, for the solution of that generalized meanreverting equation. Finally, we study a generalized meanreverting pharmacokinetic model. Contents
Maximum Likelihood Estimation for Small Noise Multiscale Diffusions
, 2013
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Quenched large deviations for multiscale diffusion processes in random environments, submitted
, 2014
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A note on highorder shorttime expansions for ATM option prices under the CGMY model
, 2013
"... The shorttime asymptotic behavior of option prices for a variety of models with jumps has received much attention in recent years. In the present work, a novel thirdorder approximation for ATM option prices under the CGMY Lévy model is derived, and extended to a model with an additional independen ..."
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The shorttime asymptotic behavior of option prices for a variety of models with jumps has received much attention in recent years. In the present work, a novel thirdorder approximation for ATM option prices under the CGMY Lévy model is derived, and extended to a model with an additional independent Brownian component. Our results shed new light on the connection between both the volatility of the continuous component and the jump parameters and the behavior of ATM option prices near expiration.