前向递归聚合系统与前向Epstein-Zin递归范式
Forward recursive aggregator systems and the forward Epstein-Zin recursive paradigm
AI总结：
本文在Itô扩散市场中提出前向递归聚合系统，统一递归效用与前向绩效准则，推导HJB SPDE、凸对偶理论，并在齐次情形下刻画前向Epstein-Zin效用过程，获得Black-Scholes和Heston模型中的显式最优策略。
AI中文摘要：
我们在Itô扩散市场中引入前向递归聚合系统，将递归效用理论与前向绩效准则理论联系起来。我们推导了相关的HJB随机偏微分方程以及一致性和可容许性的充分条件。我们还发展了一种基于状态价格密度的凸对偶理论，并识别出最优财富过程生成的密度。对于齐次聚合器，我们刻画了一类前向Epstein-Zin递归效用过程，推导了最优投资和消费策略，并在Black-Scholes和Heston模型中获得了显式解。
英文摘要：
We introduce forward recursive aggregator systems in It{ô}-diffusion markets, bridging the theories of recursive utilities and of forward performance criteria. The resulting criteria are constructed forward in time and accommodate arbitrary or rolling horizons. We derive the associated HJB SPDE and sufficient conditions for consistency and admissibility. We also develop a convex duality theory based on state price densities and identify the density generated by the optimal wealth process. For homothetic aggregators, we characterize a class of forward Epstein--Zin recursive utility processes, derive the optimal investment and consumption policies, and obtain explicit solutions in the Black and Scholes and Heston models.
