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

TL;DR

This paper derives explicit optimal consumption and investment strategies in a regime-switching market with random coefficients, using novel backward stochastic differential equations, and addresses coupled constraints on strategies.

Contribution

It introduces new BSDE systems and provides explicit solutions for optimal strategies under coupled constraints in complex market models.

Findings

Explicit optimal strategies derived for various utility functions.

New BSDE systems formulated and solved in the context of regime switching.

Addresses coupled constraints in consumption-investment problems.

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.