Systems of ergodic BSDEs arising in regime switching forward performance processes

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.

arXiv comment32 pages

References in corpus (5)

• Utility maximization in incomplete markets
• BSDE with quadratic growth and unbounded terminal value
• Quadratic BSDEs with convex generators and unbounded terminal conditions
• Number of paths versus number of basis functions in American option pricing
• Classical solutions to reaction-diffusion systems for hedging problems with interacting Ito and point processes

Cited by in corpus (1)

• A new monotonicity condition for ergodic BSDEs and ergodic control with super-quadratic Hamiltonians