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Diffusion approximations for randomly arriving expert opinions in a financial market with Gaussian drift

Published online by Cambridge University Press:  25 February 2021

Jörn Sass
Affiliation:
Technische Universität Kaiserslautern
Dorothee Westphal
Affiliation:
Technische Universität Kaiserslautern
Ralf Wunderlich
Affiliation:
Brandenburg University of Technology Cottbus-Senftenberg

Abstract

This paper investigates a financial market where stock returns depend on an unobservable Gaussian mean reverting drift process. Information on the drift is obtained from returns and randomly arriving discrete-time expert opinions. Drift estimates are based on Kalman filter techniques. We study the asymptotic behavior of the filter for high-frequency experts with variances that grow linearly with the arrival intensity. The derived limit theorems state that the information provided by discrete-time expert opinions is asymptotically the same as that from observing a certain diffusion process. These diffusion approximations are extremely helpful for deriving simplified approximate solutions of utility maximization problems.

Type
Research Papers
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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