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

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