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

Part of: Limit theorems Stochastic systems and control Mathematical finance

Published online by Cambridge University Press:  25 February 2021

Jörn Sass ,
Dorothee Westphal  and
Ralf Wunderlich
Jörn Sass*
Affiliation:
Technische Universität Kaiserslautern
Dorothee Westphal*
Affiliation:
Technische Universität Kaiserslautern
Ralf Wunderlich*
Affiliation:
Brandenburg University of Technology Cottbus-Senftenberg
*
*Postal address: Department of Mathematics, Technische Universität Kaiserslautern, P.O. Box 3049, 67653 Kaiserslautern, Germany.
*Postal address: Department of Mathematics, Technische Universität Kaiserslautern, P.O. Box 3049, 67653 Kaiserslautern, Germany.
****Postal address: Institute of Mathematics, Brandenburg University of Technology Cottbus-Senftenberg, P.O. Box 101344, 03013 Cottbus, Germany. Email address: ralf.wunderlich@b-tu.de
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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.

Keywords

Diffusion approximationsKalman filterOrnstein–Uhlenbeck processexpert opinionsportfolio optimizationpartial information

MSC classification

Primary: 91G10: Portfolio theory
Secondary: 93E11: Filtering 93E20: Optimal stochastic control 60F25: $L^p$-limit theorems
Type
Research Papers
Information
Journal of Applied Probability , Volume 58 , Issue 1 , March 2021 , pp. 197 - 216
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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