Systems of ergodic BSDEs arising in regime switching forward performance processes

TL;DR

This paper introduces ergodic BSDE systems on an infinite horizon, linking them to forward performance processes, optimal trading strategies, and long-term utility maximization in regime switching markets.

Contribution

It develops a new class of quadratic ergodic BSDE systems and connects their solutions to long-term growth rates and PDE systems with quadratic Hamiltonians.

Findings

Established existence and uniqueness of solutions to ergodic BSDE systems.

Connected ergodic BSDE solutions to utility maximization and long-term growth.

Analyzed the large-time behavior of PDE systems with quadratic growth Hamiltonians.

Abstract

We introduce and solve a new type of quadratic backward stochastic differential equation systems defined in an infinite time horizon, called \emph{ergodic 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.