论文标题
BSDE的强大控制问题与价值功能相结合
Robust control problems of BSDEs coupled with value functions
论文作者
论文摘要
在本文中考虑了一个可靠的控制问题，其中受控的随机微分方程（SDE）包括歧义参数及其系数满足非lipschitz的连续和非线性生长条件，该目标函数表示为逆向随机差分方程（BSDE），该方程（BSDE）与生成器相对于值函数。我们在适当的空间中建立了价值函数的存在和独特性，并提供了验证定理。此外，我们将结果应用于歧义在市场上解决两个典型的最佳投资问题，其中之一是Heston随机波动率模型。特别是，我们为具有歧义参数的赫斯顿模型建立了一些尖锐的估计。
A robust control problem is considered in this paper, where the controlled stochastic differential equations (SDEs) include ambiguity parameters and their coefficients satisfy non-Lipschitz continuous and non-linear growth conditions, the objective function is expressed as a backward stochastic differential equation (BSDE) with the generator depending on the value function. We establish the existence and uniqueness of the value function in a proper space and provide a verification theorem. Moreover, we apply the results to solve two typical optimal investment problems in the market with ambiguity, one of which is with Heston stochastic volatility model. In particular, we establish some sharp estimations for Heston model with ambiguity parameters.
