Optimal Consumption–Investment with Constraints in a Regime Switching Market with Random Coefficients

This paper studies finite-time optimal consumption–investment problems with power, logarithmic and exponential utilities, in a regime switching market with random coefficients and possibly subject to non-convex constraints. Compared to the existing models, one distinguish feature of our model is tha...

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Bibliographic Details
Published inApplied mathematics & optimization Vol. 91; no. 1; p. 5
Main Authors Hu, Ying, Shi, Xiaomin, Xu, Zuo Quan
Format Journal Article
LanguageEnglish
Published New York Springer US 01.02.2025
Springer Nature B.V
Springer Verlag (Germany)
Subjects
Applied mathematics
Calculus of Variations and Optimal Control; Optimization
Constraints
Consumption
Control
Differential equations
Interest rates
Investment strategy
Investments
Logarithms
Markov analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Optimization
Optimization and Control
Partial differential equations
Simulation
Systems Theory
Theoretical
Upper bounds
Utilities
Optimal consumption–investment
93E20
60H30
91G10
91B16
Regime switching
Multi-dimensional quadratic backward stochastic differential equation
Random coefficients
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Summary:This paper studies finite-time optimal consumption–investment problems with power, logarithmic and exponential utilities, in a regime switching market with random coefficients and possibly subject to non-convex constraints. Compared to the existing models, one distinguish feature of our model is that the trading constraints put on the consumption and investment strategies are coupled together in the cases of power and logarithmic utilities, leading to new technical challenges. We provide explicit optimal consumption–investment strategies and optimal values for these consumption–investment problems, which are expressed in terms of the solutions to some multi-dimensional diagonally quadratic backward stochastic differential equation (BSDE) and linear BSDE with unbound coefficients. 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.
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ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-024-10203-9