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In the present paper, given an evolving mixture of probability densities, we define a candidate diffusion process whose marginal law follows the same evolution.
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Brigo, D., and Mercurio, F. (2001b), Displaced and Mixture Diffusions for Analytically-Tractable Smile Models, in: Geman, H., Madan, D.B., Pliska, S.R., Vorst, A.C.F. (Editors), Mathematical Finance - Bachelier Congress 2000
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Alexander, C., Narayanan, S. (2001). Option Pricing with Normal Mixture Returns: Modelling Excess Kurtosis and Uncertainty in Volatility, ISMA Centre Discussion Paper 2001-10
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Brigo, D., Mercurio, F. (2000b) A Mixed-up Smile. Risk
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Brigo, D., Mercurio, F., and Sartorelli, G. (2003), Alternative asset-price dynamics and volatility smile, Quantitative Finance
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