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We introduce and solve a new type of quadratic backward stochasticdifferential equation systems defined in an infinite time horizon, called\emph{ergodic BSDE systems}. Such systems arise naturally as candidatesolutions to characterize forward performance processes and their associatedoptimal trading strategies in a regime switching market. In addition, wedevelop a connection between the solution of the ergodic BSDE system and thelong-term growth rate of classical utility maximization problems, and use theergodic BSDE system to study the large time behavior of PDE systems withquadratic growth Hamiltonians.

Systems of ergodic BSDEs arising in regime switching forward performance processes