We introduce and solve a new type of quadratic backward stochastic differential equation systems defined in an infinite time horizon  . Such systems arise naturally as candidate solutions to characterize forward performance processes and their associated optimal trading strategies in a regime switching market. We also study the asymptotic limit of the infinite horizon BSDE system, which gives arise to a novel ergodic BSDE system. In addition, we develop a connection between the solution of the ergodic BSDE system and the long-term growth rate of classical utility maximization problems  .
We introduce and solve a new type of quadratic backward stochastic differential equation systems defined in an infinite time horizon , calledergodic BSDE systems . Such systems arise naturally as candidate solutions to characterize forward performance processes and their associated optimal trading strategies in a regime switching market. In addition, we develop a connection between the solution of the ergodic BSDE system and the long-term growth rate of classical utility maximization problems , and use the ergodic BSDE system to study the large time behavior of PDE systems with quadratic growth Hamiltonians .
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, called
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ergodic BSDE systems
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We also study the asymptotic limit of the infinite horizon BSDE system, which gives arise to a novel ergodic BSDE system.
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, and use the ergodic BSDE system to study the large time behavior of PDE systems with quadratic growth Hamiltonians