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Power utility maximization with expert opinions at fixed arrival times in a market with hidden Gaussian drift

Authors: Abdelali Gabih; Hakam Kondakji; Ralf Wunderlich;

Power utility maximization with expert opinions at fixed arrival times in a market with hidden Gaussian drift

Abstract

AbstractIn this paper we study optimal trading strategies in a financial market in which stock returns depend on a hidden Gaussian mean reverting drift process. Investors obtain information on that drift by observing stock returns. Moreover, expert opinions in the form of signals about the current state of the drift arriving at fixed and known dates are included in the analysis. Drift estimates are based on Kalman filter techniques. They are used to transform a power utility maximization problem under partial information into an optimization problem under full information where the state variable is the filter of the drift. The dynamic programming equation for this problem is studied and closed-form solutions for the value function and the optimal trading strategy of an investor are derived. They allow to quantify the monetary value of information delivered by the expert opinions. We illustrate our theoretical findings by results of extensive numerical experiments.

Keywords

power utility maximization, ddc:000, Financial markets, 91G10 93E20 93E11 60G35, expert opinions, partial information, Black-Litterman model, FOS: Economics and business, Stochastic optimal control, Portfolio Management (q-fin.PM), Expert opinions, Partial information, Optimal stochastic control, Kalman-Bucy filter, stochastic optimal control, Power utility maximization, Quantitative Finance - Portfolio Management, Signal detection and filtering (aspects of stochastic processes)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
Green
hybrid