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Optimal consumption-investment with coupled constraints on consumption and investment strategies in a regime switching market with random coefficients

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  • Ying Hu
  • Xiaomin Shi
  • Zuo Quan Xu

Abstract

This paper studies finite-time optimal consumption-investment problems with power, logarithmic and exponential utilities, in a regime switching market with random coefficients, subject to coupled constraints on the consumption and investment strategies. We provide explicit optimal consumption-investment strategies and optimal values for the problems in terms of the solutions to some diagonally quadratic backward stochastic differential equation (BSDE) systems and linear BSDE systems with unbound coefficients. Some of these BSDEs are new in the literature and solving them is one of the main theoretical contributions of this paper. We accomplish the latter by applying the truncation, approximation technique to get some a priori uniformly lower and upper bounds for their solutions.

Suggested Citation

  • Ying Hu & Xiaomin Shi & Zuo Quan Xu, 2022. "Optimal consumption-investment with coupled constraints on consumption and investment strategies in a regime switching market with random coefficients," Papers 2211.05291, arXiv.org.
    • Handle: RePEc:arx:papers:2211.05291
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    References listed on IDEAS

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    Cited by:

    1. Panpan Zhang & Zuo Quan Xu, 2023. "Multidimensional indefinite stochastic Riccati equations and zero-sum linear-quadratic stochastic differential games with non-markovian regime switching," Papers 2309.05003, arXiv.org.

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