Systems of Ergodic BSDEs Arising in Regime Switching Forward Performance Processes

Ying Hu · Gechun Liang · Shanjian Tang

21 citations0/0 files storedSIAM Journal on Control and Optimization

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Stochastic processes and financial applications Economic theories and models Risk and Portfolio Optimization

Abstract

We introduce and solve a new type of quadratic backward stochastic differential equation (BSDE) systems defined in an infinite time horizon, called 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.

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References

1997Backward Stochastic Differential Equations in Finance 2000Backward stochastic differential equations and partial differential equations with quadratic growth 1997Backward stochastic differential equations and integral-partial differential equations 2005Utility maximization in incomplete markets 2006BSDE with quadratic growth and unbounded terminal value 2007Quadratic BSDEs with convex generators and unbounded terminal conditions 2007Solvability of backward stochastic differential equations with quadratic growth 2008Quadratic BSDEs with convex generators and unbounded terminal conditions

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2022Constrained stochastic LQ control with regime switching and application to portfolio selection 2023Stochastic Linear-Quadratic Optimal Control Problems with Random Coefficients and Markovian Regime Switching System

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