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Optimal consumption with Hindy–Huang–Kreps preferences under nonlinear expectations

Part of: Stochastic systems and control Probabilistic methods, simulation and stochastic differential equations Mathematical economics Stochastic analysis

Published online by Cambridge University Press:  14 June 2022

Giorgio Ferrari ,
Hanwu Li Open the ORCID record for Hanwu Li [Opens in a new window]  and
Frank Riedel
Giorgio Ferrari*
Affiliation:
Bielefeld University
Hanwu Li*
Affiliation:
Shandong University
Frank Riedel*
Affiliation:
Bielefeld University and University of Johannesburg
*
*Postal address: Center for Mathematical Economics, Universtätstrasse 25, Bielefeld, Germany.
***Postal address: Research Center for Mathematics and Interdisciplinary Sciences, Binhai Rd 72, Qingdao, China. Email address: [email protected]
*Postal address: Center for Mathematical Economics, Universtätstrasse 25, Bielefeld, Germany.
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Abstract

We study an intertemporal consumption and portfolio choice problem under Knightian uncertainty in which agent’s preferences exhibit local intertemporal substitution. We also allow for market frictions in the sense that the pricing functional is nonlinear. We prove existence and uniqueness of the optimal consumption plan, and we derive a set of sufficient first-order conditions for optimality. With the help of a backward equation, we are able to determine the structure of optimal consumption plans. We obtain explicit solutions in a stationary setting in which the financial market has different risk premia for short and long positions.

Keywords

Knightian uncertaintyg-expectationambiguity aversionsingular stochastic control

MSC classification

Primary: 93E20: Optimal stochastic control 91B42: Consumer behavior, demand theory
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.) 65C30: Stochastic differential and integral equations
Type
Original Article
Information
Advances in Applied Probability , Volume 54 , Issue 4 , December 2022 , pp. 1222 - 1251
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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