模型不确定性下带非熵惩罚的最优随机控制问题
Optimal stochastic control problem under model uncertainty with non-entropic penalty
摘要：
研究了模型不确定性下带一般惩罚项的随机控制问题。考虑了两种类型的处罚。第一种是在连续过滤的一般框架中处理的f-发散惩罚类型。第二个是在布朗过滤的背景下研究的一致时间惩罚。在一致时间惩罚的情形下，我们将随机控制问题的值过程刻画为一类具有无界终端条件的二次倒向随机微分方程的唯一解。
英文摘要：
In this paper, a stochastic control problem under model uncertainty with general penalty term is studied. Two types of penalties are considered. The first one is of type f-divergence penalty treated in the general framework of a continuous filtration. The second one called consistent time penalty studied in the context of a Brownian filtration. In the case of consistent time penalty, we characterize the value process of our stochastic control problem as the unique solution of a class of quadratic backward stochastic differential equation with unbounded terminal condition.
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