一类带退化系数的约束控制问题和带奇异终端条件的退化倒向SPDE
A Constrained Control Problem with Degenerate Coefficients and Degenerate Backward SPDEs with Singular Terminal Condition
摘要：
本文研究了在市场冲击下最优资产组合清算模型中的一类带约束的最优控制问题。系数可以是随机的，在这种情况下，值函数由具有奇异终端条件的退化倒向随机偏微分方程（BSPDE）描述。对于这种退化的BSPDE，我们证明了非负解的存在性和唯一性。我们的存在性结果需要一个新的梯度估计退化BSPDE。
英文摘要：
We study a constrained optimal control problem with possibly degenerate coefficients arising in models of optimal portfolio liquidation under market impact. The coefficients can be random in which case the value function is described by a degenerate backward stochastic partial differential equation (BSPDE) with singular terminal condition. For this degenerate BSPDE, we prove existence and uniqueness of a nonnegative solution. Our existence result requires a novel gradient estimate for degenerate BSPDEs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
