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Optimal entry and consumption under habit formation

Part of: Mathematical finance Stochastic systems and control Hamilton-Jacobi theories, including dynamic programming

Published online by Cambridge University Press:  10 March 2022

Yue Yang  and
Xiang Yu Open the ORCID record for Xiang Yu [Opens in a new window]
Yue Yang*
Affiliation:
The Hong Kong Polytechnic University
Xiang Yu*
Affiliation:
The Hong Kong Polytechnic University
*
*Postal address: Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong.
*Postal address: Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong.
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Abstract

This paper studies a composite problem involving decision-making about the optimal entry time and dynamic consumption afterwards. In Stage 1, the investor has access to full market information subject to some information costs and needs to choose an optimal stopping time to initiate Stage 2; in Stage 2, the investor terminates the costly full information acquisition and starts dynamic investment and consumption under partial observation of free public stock prices. Habit formation preferences are employed, in which past consumption affects the investor’s current decisions. Using the stochastic Perron method, the value function of the composite problem is proved to be the unique viscosity solution of some variational inequalities.

Keywords

Optimal entry problemconsumption habit formationstochastic Perron methodviscosity solution

MSC classification

Primary: 91G10: Portfolio theory 49L25: Viscosity solutions
Secondary: 93E11: Filtering 93E20: Optimal stochastic control 49L20: Dynamic programming method
Type
Original Article
Information
Advances in Applied Probability , Volume 54 , Issue 2 , June 2022 , pp. 433 - 459
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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