文章基本信息

标题：Affine Transformations of Itô Diffusions and their Transition Densities
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作者：Sanae RUJIVAN
期刊名称：Walailak Journal of Science and Technology (WJST)
印刷版ISSN：2228-835X
出版年度：2011
卷号：8
期号：1
页码：71-79
DOI：10.2004/wjst.v8i1.13
语种：English
出版社：Institute of Research and Development, Walailak University.
摘要：For a given Itô diffusion, we derive the forward Kolmogorov equation (FKE) associated with the adjoint operator of the infinitesimal generator of an affine transformation of the given Itô diffusion. The fundamental solution obtained by solving the FKE is, in fact, the transition density of the transformed diffusion. Moreover, we prove that the transition density can be represented in terms of a product of two functions, a Jacobian term and a composition of the transition density of the given Itô diffusion and the inverse of the transformation. Finally, we present an application of our results in parameter estimation in commodity markets in which the commodity prices are assumed to follow an extended Black-Scholes model.
关键词：Itô diffusions, forward Kolmogorov equation, transition densities