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|Title: ||Nearly recombining processes and the calculation of expectations|
|Authors: ||van den Berg, Imme|
|Keywords: ||Discrete stochastic processes|
|Issue Date: ||2008|
|Abstract: ||In the context of Nonstandard Analysis, we study stochastic difference equations with infinitesimal time-steps. In particular we give a necessary and sufficient condition for a solution to be nearly-equivalent to a recombining stochastic process. The characterization is based upon a partial differential equation involving the trend and the conditional variance of the original process. An analogy with Ito's Lemma is pointed out. As an application we obtain a method for approximation of expectations, in terms of two ordinary differential equations, also involving the trend and the conditional variance of the original process, and of Gaussian integrals.|
|Appears in Collections:||MAT - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica|
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