Utility maximization under partial information with expert opinions
Project partners
- Prof. Dr. Rüdiger Frey, Vienna University of Economics and Business, Austria
- Prof. Dr. Jörn Sass, University of Kaiserslautern
- Prof. Abdelali Gabih, Chouaib Doukkali University, El Jadida, Morocco
Keywords
- Portfolio optimization
- Partial information
- Stochastic optimal control
- Expert opinions
Project description
Portfolio optimization is one of the cornerstones of modern financial mathematics. It deals with the optimal allocation of investment assets across various securities in a financial market. Solving such problems plays a central role in many practical issues in the banking and insurance industries.
In this project, utility maximization problems are solved in a continuous-time financial market with partial information about drift, where expert opinions about the unobservable drift are also available. For this purpose, the drift must be estimated from observable variables. Such estimates based on historical security prices are often too inaccurate. Therefore, investors use additional information to estimate the drift, e.g., economic news, company reports, recommendations from financial analysts, ratings from rating agencies, and their own intuitive assessment of future price developments. These external sources of information, referred to as expert opinions, are combined with observations of security prices to improve the drift estimate.
Solutions to the above portfolio optimization problem are sought for logarithmic and power utility functions and for models in which the drift is described by an unobservable Ornstein-Uhlenbeck process or a continuous-time Markov chain.
The mathematical contribution of this project is the analytical characterization of the dynamic programming equations (DPEs) that arise in the above stochastic optimal control problems. These DPEs form a sequence of nonlinear partial differential equations or are given by partial integro-differential equations. By solving these equations, the optimal investment strategies can be determined. Suitable numerical methods are being developed for this purpose.
From a financial perspective, the project will contribute to a better understanding of the economic value of the additional information contained in expert opinions.
Project-related publications
- R. Frey, A. Gabih, R. Wunderlich: Portfolio optimization under partial information with expert opinions. International Journal of Theoretical and Applied Finance, Vol. 15, No. 1 (2012)
- Gabih, H. Kondakji, J. Sass, R. Wunderlich: Expert Opinions and Logarithmic Utility Maximization in a Market with Gaussian Drift. Communications on Stochastic Analysis, Vol. 8, No. 1, 27-47, 2014
- R. Frey, A. Gabih, R. Wunderlich: Portfolio Optimization under Partial Information with Expert Opinions: a Dynamic Programming Approach. Communications on Stochastic Analysis , Vol. 8, No. 1, 49-79, 2014
- J. Sass, D. Westphal, R. Wunderlich: Expert Opinions and Logarithmic Utility Maximization for Multivariate Stock Returns with Gaussian Drift. International Journal of Theoretical and Applied Finance, 20, 1750022, 2017
- Gabih, H. Kondakji, R. Wunderlich: Asymptotic filter behavior for high-frequency expert opinions in a market with Gaussian drift. Stochastic Models. 36:4, 519-547, 2020
- J. Sass, D. Westphal, R. Wunderlich: Diffusion approximations for randomly arriving expert opinions in a financial market with Gaussian drift. Journal of Applied Probability, 58 (1), 197 - 216, 2021
- J. Sass, D. Westphal, R. Wunderlich: Diffusion approximations for periodically arriving expert opinions in a financial market with Gaussian drift. Stochastic Models 2022, DOI: 10.1080/15326349.2022.2100423
- Gabih, H. Kondakji, R. Wunderlich: Well Posedness of Utility Maximization Problems Under Partial Information in a Market with Gaussian Drift. arXiv:2205.08614 [q-fin.PM] (2022)
- Gabih, H. Kondakji, R. Wunderlich: Power utility maximization with expert opinions at fixed arrival times in a market with hidden Gaussian drift. Annals of Operations Research, 341, 897–936, 2024
- A. Gabih, R. Wunderlich
Portfolio optimization in a market with hidden Gaussian drift and randomly arriving expert opinions. Annals of Operations Research, 2025