Portfolio Optimization for a Large Investor Controlling Market Sentiment Under Partial Information

37 Pages Posted: 15 Jun 2017  

Sühan Altay

Vienna University of Technology - Financial and Actuarial Mathematics Research Group

Katia Colaneri

University of Perugia, Department of Economics

Zehra Eksi

Vienna University of Economics and Business, Institute for Statistics and Mathematics

Date Written: June 14, 2017

Abstract

We consider an investor faced with the utility maximization problem in which the risky asset price process has pure-jump dynamics affected by an unobservable continuous-time finite-state Markov chain, the intensity of which can also be controlled by actions of the investor. Using the classical filtering theory, we reduce this problem with partial information to one with full information and solve it for logarithmic and power utility functions. In particular, we apply control theory for piece-wise deterministic Markov processes (PDMP) to our problem and derive the optimality equation for the value function and characterize the value function as the unique viscosity solution of the associated dynamic programming equation. Finally, we provide a toy example, where the unobservable state process is driven by a two-state Markov chain, and discuss how investor's ability to control the intensity of the state process affects the optimal portfolio strategies as well as the optimal wealth under both partial and full information cases.

Keywords: utility maximization, regime-switching, market sentiment, partial information, piece-wise deterministic Markov processes

JEL Classification: C02, C44, C61, G11

Suggested Citation

Altay, Sühan and Colaneri, Katia and Eksi, Zehra, Portfolio Optimization for a Large Investor Controlling Market Sentiment Under Partial Information (June 14, 2017). Available at SSRN: https://ssrn.com/abstract=2986612

Sühan Altay

Vienna University of Technology - Financial and Actuarial Mathematics Research Group ( email )

Karlsplatz 13
A-1040 Vienna
Austria

Katia Colaneri

University of Perugia, Department of Economics ( email )

Via Pascoli 22
Perigoa, 06121
Italy

Zehra Eksi (Contact Author)

Vienna University of Economics and Business, Institute for Statistics and Mathematics ( email )

Welthandelsplatz 1
Building D4, 4th floor
Vienna, 1020
Austria

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