SIAM Journal on Control and Optimization, Volume 58, Issue 4, Page 2503-2534, January 2020.
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.

中文翻译：

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体制转换中的遍历式BSDE系统向前转换性能过程

SIAM控制与优化杂志，第58卷，第4期，第2503-2534页，2020年1月。
我们引入并解决了在无限时域内定义的一种新型二次反向随机微分方程（BSDE）系统，称为遍历BSDE系统。这样的系统作为候选解决方案自然而然地出现，以表征制度转换市场中的远期业绩过程及其相关的最佳交易策略。此外，我们建立了遍历BSDE系统的解与经典效用最大化问题的长期增长率之间的联系，并使用遍历BSDE系统研究了具有二次增长哈密顿量的PDE系统的长时间行为。