An analytical characterization for an optimal change of Gaussian measures
type: Item
instance of: scholarly article
title: An analytical characterization for an optimal change of Gaussian measures
zbMATH Open document ID: 1158.60363
DOI: 10.1155/JAMDS/2006/95912
author: Henry Schellhorn
published in: Journal of Applied Mathematics and Decision Sciences
publication date: 2008-11-20T00:00:00Z
full work available at URL: https://eudml.org/doc/129743
review text: Summary: We consider two Gaussian measures. In the ``initial'' measure the state variable is Gaussian, with zero drift and time-varying volatility. In the ``target measure'' the state variable follows an Ornstein-Uhlenbeck process, with a free set of parameters, namely, the time-varying speed of mean reversion. We look for the speed of mean reversion that minimizes the variance of the Radon-Nikodým derivative of the target measure with respect to the initial measure under a constraint on the time integral of the variance of the state variable in the target measure. We show that the optimal speed of mean reversion follows a Riccati equation. This equation can be solved analytically when the volatility curve takes specific shapes. We discuss an application of this result to simulation, which we presented in an earlier article.
Mathematics Subject Classification ID: 60H30
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 91B28
zbMATH DE Number: 5369132
describes a project that uses: GAUSSIAN
MaRDI profile type: Publication
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OpenAlex ID: W2088146118
description: scientific article; zbMATH DE number 5369132